Into Math Grade 8 Module 13 Lesson 3 Answer Key Find Volume of Spheres

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HMH Into Math Grade 8 Module 13 Lesson 3 Answer Key Find Volume of Spheres

I Can find the volume of a sphere and the dimensions of a sphere given its volume.

Step It Out

Question 1.
A sphere is a three-dimensional figure with all points the same distance from the center. The radius of a sphere is the distance from the center to any point on the sphere.
You can use the following reasoning to develop a formula for the volume of a sphere.

A. Start with a sphere of radius r. How is the height of the sphere related to the radius?
h = __________ r
Answer:

h = 2r

B. Consider a cylinder with the same radius and the same height as the sphere.

Imagine filling the sphere with sand and pouring the sand into the cylinder. The sand will fill \(\frac{2}{3}\) of the cylinder.

Answer:
The volume of Sphere = Volume of Cylinder – Volume of Cone
As we know, the volume of cylinder = πr²h and volume of cone = one-third of the volume of cylinder = (1/3)πr²h
The volume of Sphere = Volume of Cylinder – Volume of Cone
⇒ Volume of Sphere = πr²h – (1/3)πr²h = (2/3)πr²h
In this case, height of cylinder = diameter of sphere = 2r
Hence, volume of sphere is (2/3)πr²h = (2/3)πr²(2r) = (4/3)πr³

Turn and Talk How is the formula for the volume of a sphere similar to the formula for the volume of a cone? How is it different?
Answer:
– the volume of cone = one-third of the volume of cylinder = (1/3)πr²h
– A sphere is a solid round three-dimensional figure, where every point on its surface is equidistant from its centre. So all the radii of a sphere are equal.

Question 2.
You can use this formula to find the volume of a sphere when you are given or can calculate its radius.

A. Approximate the volume of the sphere. Use \(\frac{22}{7}\) for π and leave your answer as an improper fraction.
To find the volume, use the volume formula with
r = ___________.
V = \(\frac{4}{3}\) πr³
≈ \(\frac{4}{3}\) (\(\frac{22}{7}\)) (__________)²
≈ \(\frac{4}{3}\) (\(\frac{22}{7}\)) (__________)
≈ _________
The volume of the sphere is approximately ___________ cubic inches.
Answer:
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
Volume of Sphere, V = (4/3)πr³
The given dimension:
r = 7
v = 4/3 x 22/7 x 7 x 7 x 7
V = 4/3 x 22 x 49
V = 1437 (approximately)
Therefore, the volume of the sphere is 1437 cubic inches.

B. Approximate the volume of Earth. Use 3.14 for π. Express your answer in scientific notation, rounding the first factor to the nearest tenth.

To find the volume, use the volume formula with
r = ___________
V = \(\frac{4}{3}\) πr³
= \(\frac{4}{3}\) π(__________ × __________)³
= \(\frac{4}{3}\) π(__________)³ × (__________)³
≈ \(\frac{4}{3}\) (3.14) (__________) ×
≈ ________ ×
≈ _________ ×
The volume of Earth is approximately ___________ cubic kilometers.
Answer:
The given dimension:
r = 6.4 x 10^3 km
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
Volume of Sphere, V = (4/3)πr³
V = 4/3 x 22/7 x 6400000000
V =2.6794666624 × 10¹⁰
Therefore, the volume of the earth is 2.6794666624 × 10^10.

Turn and Talk At what points did you use a property of exponents in simplifying the expression for the volume in Part B? What property or properties did you use?
Answer:
Step 1: Put a decimal point after the first digit of the number from the left. If there is only one digit in a number excluding zeros, then we don’t need to put decimal.
Step 2: Multiply that number with a power of 10 such that the power will be equal to the number of times we shift the decimal point.

Question 3.
You can find the volume of a sphere if you know its diameter.

A. Find the exact volume of the spherical rubber-band ball. Leave your answer in terms of π.
The diameter of the sphere is ___________ centimeters.
So, the radius of the sphere is ___________ centimeters.
V = \(\frac{4}{3}\) πr³
= \(\frac{4}{3}\) π (____________)³
= \(\frac{4}{3}\) π (_____________)
= ____________
The volume of the sphere is ____________ cubic centimeters.
Answer:
The volume of the diameter is 12 cms
so, the radius is diameter/2 = 12/2 = 6 cms
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
Volume of Sphere, V = (4/3)πr³
V = 4/3 x π  x 6 x 6 x 6
V = 4/3 x π x 216
V = 288π
Therefore, the volume of the sphere is 288π cubic centimetres.

B. Approximate the volume of a sphere with a diameter of 7.4 millimeters. Use 3.14 for π. Round the volume to the nearest tenth.
The radius of the sphere is ____________ millimeters.
V = \(\frac{4}{3}\) πr³
= \(\frac{4}{3}\) π (____________)³
≈ \(\frac{4}{3}\) (__________) (____________)
≈ ___________
Answer:
The above-given dimensions:
diameter = 7.4 mm
r = d/2 = 7.4/2 = 3.7
The radius of the sphere is 3.7 mm
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
Volume of Sphere, V = (4/3)πr³
V = 4/3 x 3.14 x (3.7)^3
V = 4/3 x 3.14 x 51
V = 213.52 cubic mm
Therefore, the volume of the sphere is 213.52 cubic mm
Check Understanding

Question 1.
In the figure, the sphere fits perfectly inside the cylinder, with the top and bottom of the sphere just touching the bases of the cylinder. How does the volume of the sphere compare to the volume of the cylinder?

Answer:

We must now make the cylinder’s height 2r so the sphere fits perfectly inside.
So the sphere’s volume is 4/3 vs 2 for the cylinder
Or more simply the sphere’s volume is 2/3 of the cylinder’s volume.
The volume of the cylinder = πr²h
Now substitute 2r in the place of h.
V = π x r^2 x 2r = 2πr^3
spheres volume = 2/3 x 2πr^3
The volume of the sphere is 4/3πr^3.

Question 2.
Approximate the volume of a sphere with a diameter of 20 meters. Leave your answer in terms of π. Then use 3.14 for π and round the volume to the nearest tenth.
Answer:
The given dimension:
diameter = 20 metres
radius = d/2 = 20/2 = 10metres.
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
Volume of Sphere, V = (4/3)πr³
Substitute the values in the formula.
V = 4/3 x 3.14 x (10)^3
V = 4/3 x 3.14 x 1000
V = 4/3 x 3140
V = 4186.66667
approximately 4187
Therefore, the volume of the sphere is 4187 cubic metres.

On Your Own

Question 3.
A sphere has a radius of 5 feet.
A. Find the volume of the sphere. Leave your answer in terms of π. Then use 3.14 for π and round the volume to the nearest tenth.
Answer:
The given dimension:
radius = 5 feet
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
Volume of Sphere, V = (4/3)πr³
V = 4/3 x π x 125
V = 166.66667π
approximately, 167π
Therefore, the volume of the sphere in terms of π is 167π.
And then if we place π value.
V = 167 x 3.14
V = 524.38
The nearest tenth place is 525.
Therefore, the volume of the sphere is 525 cubic feet.

B. Construct Arguments Explain how you can use estimation to justify that the volume you found is reasonable.

Answer:
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
Volume of Sphere, V = (4/3)πr³
V = 4/3 x 3.14 x (12)^3
V = 4/3 x 3.14 x 1728
V = 7234.56
The estimation is 8000.
therefore, the volume of a sphere is 7235 cubic cms.
if the place value is less than 5 it remains the same. And if it is greater than 5 or equal to 5 then we put all zeroes and we add 1.

Question 4.
Approximate the volume of the basketball. Use \(\frac{22}{7}\) for π and round the volume to the nearest tenth.
Answer:

 

For Problems 5-10, approximate the volume of each sphere. Use 3.14 for π and round the volume to the nearest tenth.

Question 5.

Answer:
The given dimension:
radius = 2
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
Volume of Sphere, V = (4/3)πr³
V = 4/3 x 3.14 x (2)^3
V = 4/3 x 3.14 x 8
V = 33.49333
The nearest tenth value is 33.
Therefore, the volume of the sphere is 33 cubic inches.

Question 6.

Answer:
The given dimension:
radius = 4.8
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
Volume of Sphere, V = (4/3)πr³
V = 4/3 x 3.14 x (4.8)^3
V = 463.011
The nearest tenth value is 463 cubic mm
Therefore, the volume of the sphere is 463 cubic mm

Question 7.

Answer:
The given dimension:
radius = 17m
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
Volume of Sphere, V = (4/3)πr³
V = 4/3 x 3.14 x (17)^3
V = 4/3 x 3.14 x 4913
V = 20569.0933
The nearest tenth value is 20569
Therefore, the volume of the sphere is 20569 cubic m

Question 8.

Answer:
height of cylinder = diameter of sphere = 2r
Hence, volume of sphere is (2/3)πr²h = (2/3)πr²(2r) = (4/3)πr³
2r = 1
r = 1/2
V  = 4/3 x 3.14 x (1/2)^3
V = 4/3 x 3.14 x 0.125
V = 0.52
Therefore, the volume of a sphere is 0.52 cubic yards.
(or)
we can use this formula also.
V = (πd³)/6.
d = 2r = 1
V = 3.14 x 1/6
V = 0.52 cubic yards

Question 9.

Answer:
The given dimension:
diameter = 6.2 cm
radius = d/2 = 6.2/2 = 3.1
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
Volume of Sphere, V = (4/3)πr³
V = 4/3 x 3.14 x (3.1)^3
V = 4/3 x 3.14 x 30 (approximately)
V = 125.6 cubic cm

Question 10.

Answer:
height of cylinder = diameter of sphere = 2r
Hence, volume of sphere is (2/3)πr²h = (2/3)πr²(2r) = (4/3)πr³
2r = 3
r = 3/2
V = 4/3 x 3.14 x (3/2)^3
V = 4/3 x 3.14 x 3.375
V = 4/3 x 10.5975
V = 14.13
approximately 14.
The volume of the sphere is 14 cubic inches

For Problems 11-12, use the spherical marble shown.

Question 11.
Attend to Precision What is the exact volume? Leave your answer in terms of π. Round the first factor in scientific notation to the nearest tenth.
Answer:
The given dimension:
radius = 5 x 10^-3
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
Volume of Sphere, V = (4/3)πr³
V = 4/3 x π x (5 x 10^-3)^3
V = 4/3 x π x 0.000000005
V = 0.00000000666666667π
The scientific notation is 6.66666667 × 10^-9

Question 12.
Find the volume of the marble to the nearest cubic millimetre using \(\frac{22}{7}\) for π. Explain your method.
Answer:
Here we use the same method as above, but we substitute π value in the place of π.
By using the same radius we get the volume:
V = 0.00000000666666667π
Here we need to substitute the π  value.
V = 0.00000000666666667 x 3.14
V = 2.09333333E-8 cubic m
The scientific notation is 2.09333333 × 10^-8

For Problems 13-18, approximate the volume of each sphere. Use 3.14 for π and round the first factor in scientific notation to the nearest tenth.

Question 13.

Answer:
The given dimension:
radius = 6 x 10^4
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
Volume of Sphere, V = (4/3)πr³
V = 4/3 x 3.14 x (6 x 10^4)^3
V = 4/3 x 3.14 x 6000000000000
V = 25120000000000
For that, we need to write the scientific notation
the scientific notation is 2.512 × 10¹³
Therefore, the volume of the sphere is 2.512 × 10^13 cubic kilometres

Question 14.

Answer:
The given dimension:
radius = 2.1 x 10^8
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
The volume of Sphere, V = (4/3)πr^3
V = 4/3 x 3.14 x (2.1 x 10^8)^3
V = 4/3 x 3.14 x 2100000000000000000000000
V = 8792000000000000000000000
The scientific notation is 8.792 x 10^24
Therefore, the volume of the sphere is 8.792 x 10^24 cubic mm

Question 15.

Answer:
The given dimension:
radius = 7.2 x 10^-4 ft
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
The volume of Sphere, V = (4/3)πr^3
V = 4/3 x 3.14 x (7.2 x 10^-4)^3
V = 4/3 x 3.14 x 0.0000000000072
V = 0.000000000030144 cubic ft
The scientific notation is 3.0144 × 10^-11 cubic feet.

Question 16.

Answer:
The given dimension:
2r = 6 x 10^-2
r = 6 x 10^-2/2
r = 0.000006
r = 6 x 10^-6
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
The volume of Sphere, V = (4/3)πr^3
V = 4/3 x 3.14 x (6 x 10^-6)^3
V = 4/3 x 3.14 x (6 x 10^-18)
V = 4/3 x 3.14 x 0.000000000000000006
V = 0.00000000000000002512
The scientific notation is 2.512 x 10^-17 cubic metres.

Question 17.

Answer:
The given dimension:
diameter = 8.4 x 10^7 km
radius = d/2 = 8.4 x 10^7/2
r = 2.65631323 × 10^4
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
The volume of Sphere, V = (4/3)πr^3
V = 4/3 x 3.14 x ( 2.65631323 × 10^4)^3
V = 4/3 x 3.14 x 2656313230000
V = 1.11210981 × 10^13 cubic km
Question 18.

Answer:
The given dimension:
diameter = 1.2 x 10^8 m
radius = d/2 = 1.2 x 10^8/2
r = 60000000 = 6 x 10^7 m
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
The volume of Sphere, V = (4/3)πr^3
V = 4/3 x 3.14 x (6 x 10^7)^3
V = 4/3 x 3.14 x 6000000000000000000000
V = 4/3 x 3.14 x (6 x 10^21)
V = 25120000000000000000000
The scientific notation is 2.512 × 10^22 cubic metres.

Question 19.
Open-Ended In the photo, V represents the volume of the spherical plant shown. Determine a possible radius for the sphere. Justify your answer.

Answer:
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
The volume of Sphere, V = (4/3)πr^3
Volume = 4000 cubic inches
4000 = 4/3 x 3.14 x r^3
4000 = 4.18 x r^3
r^3 = 4000/4.18
r^3 =957
r = 9.855
Therefore, the possible radius is 9.855 inches

Question 20.
Use Tools You can measure the diameter of a spherical object by putting the object on a flat surface and placing blocks or books on either side of the object, as shown. Then use a ruler to measure the distance between the blocks or books. Find a spherical object, measure its diameter, and find its volume. Describe the object, and give its diameter and volume.

Answer:
The general formula for the volume of a sphere in terms of its radius is given as V = (4/3) π r³. Let’s say ‘d’ is its diameter, according to the definition of diameter, we have d = 2r. From this, we get the value of radius = (d/2). Substituting this in the volume of a sphere formula, the volume of a sphere in terms of diametre is represented as V = (πd³)/6.
For suppose, the diameter is 6 cm
V = (3.14 x 6^3)/6
V = 678.24/6
V = 113.04 cubic cms.

Question 21.
When you cut a sphere in half by passing a plane through its center, the result is a hemisphere.

A. Write a formula for the volume V of a hemisphere. Explain how you found it.
Answer:
The volume of a hemisphere = (2/3)πr³ cubic units.
Let us see how the formula for the volume of a hemisphere is derived. Since a hemisphere is half of a sphere, we can divide the volume of a sphere by 2 to get the volume of its hemisphere. Now considering that the radius of a sphere is r.
The volume of the sphere can be calculated using the formula, Volume of Sphere = 4πr³/3. So, the volume of a hemisphere = 1/2 of 4πr³/3 = 1/2 × 4πr³/3 = 2πr³/3

B. Find the volume of the hemisphere shown. Leave your answer in terms of π. Then use 3.14 for π and round the volume to the nearest tenth.
Answer:
The given dimension:
radius = 12 ft
The volume of hemisphere = 2πr³/3
V = 2 x π x 12 x 12 x 12/3
V = 3456π/3
V = 1152π
Therefore, the volume of the hemisphere in terms of π is 1152π cubic ft

C. Approximate the volume of a hemisphere with a diameter of 6.2 meters. Use 3.14 for π and round the volume to the nearest tenth.
Answer:
The given dimension:
diameter = 6.2 m
r = d/2 = 6.2/2 = 3.1 m
The volume of hemisphere = 2πr³/3
V = 2 x 3.14 x 3.1 x 3.1 x 3.1/3
V = 187.1/3
V = 62.3666667
The nearest tenth value is 62.4
Therefore, the volume of the hemisphere is 62.4 cubic metres.

Question 22.
Critique Reasoning A student said that when you double the radius of a sphere, you double the volume of the sphere. Do you agree or disagree? Give one or more specific examples to justify your answer.
Answer:
I definitely agree.
if a radius is doubled automatically, the sphere volume also increases.
– If the radius of a circle is doubled, the area of the circle will be quadrupled and the circumference will also be doubled.

Lesson 13.3 More Practice/Homework

Question 1.
Construct Arguments The spherical and the cylindrical candles have shown to have the same radius and the same height. The volume of the cylindrical candle is 6 cubic centimetres. What is the volume of the spherical candle? Explain.

Answer:
The volume of the cylindrical candle = 6 cubic cms
h = r
The volume of the cylinder = πr^2h
Volume of cylinder = πr^2 x r = πr^3 = 6 cubic cms
We need to find out the volume of the spherical candle.
The volume of sphere = (4/3)πr^3
V = 4/3 x 6
V = 8 cubic cms.
therefore, the volume of sphere is 8 cubic cms.

Question 2.
Math on the Spot Approximate the volume of a sphere with a radius of 7 feet, both in terms of π and to the nearest tenth. Use 3.14 for π.
Answer:
Given dimension:
radius = 7 feet
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
The volume of Sphere, V = (4/3)πr^3
V = 4/3 x π x 7 x 7 x 7
v = 457.333π
The nearest tenth value is 457.3π
The volume of the sphere in terms of π is 457.3π
Now substitute the π value in the place of π
V = 457.3 x 3.14
V = 1435.922
The nearest tenth value is 1435.9 cubic feet.

For Problems 3-6, approximate the volume of the sphere. Use 3.14 for π and round the volume to the nearest tenth.

Question 3.

Answer:
Given dimension:
radius = 7.5 in
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
The volume of Sphere, V = (4/3)πr^3
V = 4/3 x 3.14 x 7.5 x 7.5 x 7.5
V = 1766.25
The nearest tenth value is 1766.3
Therefore, the volume of the sphere is 1766.3 cubic inches

Question 4.

Answer:
Given dimension:
radius = 20mm
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
The volume of Sphere, V = (4/3)πr^3
V = 4/3 x 3.14 x 20 x 20 x 20
V =4/3 x 3.14 x 8000
V = 33493.3333
The nearest tenth value is 33493.3
Therefore, the volume of the sphere is 33493.3 cubic mm

Question 5.

Answer:
Given dimension:
diameter = 7.8 cm
r = d/2 = 7.8/2 = 3.9 cm
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
The volume of Sphere, V = (4/3)πr^3
V = 4/3 x 3.14 x 3.9 x 3.9 x 3.9
V = 248.34888
The nearest tenth value is 248.3
Therefore, the volume of the sphere is 248.3 cubic cms

Question 6.

Answer:
d = 2r = 5.6
V = (πd³)/6.
V = (3.14 x 5.6^3)/6
V = 551.43424/6
V = 91.9057067
The nearest tenth value is 91.9
Therefore, the volume of sphere = 91.9 cubic m

Question 7.
Critique Reasoning A student was asked to find the exact volume of the sphere shown, leaving the answer in terms of π. The student’s work is shown. Explain the student’s error.

V = \(\frac{4}{3}\) π(6)³ = \(\frac{4}{3}\) π(6)³ = \(\frac{4}{3}\) π(216) = 288π ft³
Answer:
Given dimension:
diameter = 6ft
r = d/2 = 6/2 = 3 ft
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
The volume of Sphere, V = (4/3)πr^3
V = 4/3 x π x 3 x 3 x 3
V = 4 x π x 9
V = 36π
Therefore, the volume of the sphere is 36π cubic ft.
The student’s error was he directly substituted the diameter in the formula without finding the radius. That’s why he got the error. The correct explanation is above.

Test Prep

Question 8.
A sphere has a diameter of 14.6 feet. Fill in the formula for the volume of the sphere by writing a numerical value in each box.

Answer:
Given dimension:
diameter = 14.6 ft
r = d/2 = 14.6/2 = 7.3 ft
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
The volume of Sphere, V = (4/3)πr^3
V = 4/3 x 3.14 x 7.3 x 7.3 x 7.3
V = 4/3 x 3.14 x 389.017
V = 1628.68451
The nearest tenth value is 1628.7
Therefore, the volume of the sphere is 1628.7 cubic ft

Question 9.
A student has a set of six spheres with radii 1, 2, 3, 4, 5, and 6 centimetres. Which of the following is the volume of a sphere in the set? Select all that apply.
(A) \(\frac{4}{3}\) π cm³
(B) \(\frac{8}{3}\) π cm³
(C) \(\frac{32}{3}\) π cm³
(D) 36π cm³
(E) 125π cm³
(F) 288π cm³
Answer: Options A, D, and F are correct.
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
The volume of Sphere, V = (4/3)πr^3
for radius 1:
V = 4/3 x π x 1 = 4/3πcubic cm
for radius 2:
V = 4/3 x π x 8 = 10.7 cubic cm
for radius 3:
V = 4/3 x π x 27 = 36π cubic cm
for radius 4:
V = 4/3 x π x 64 = 85.3π cubic cm
for radius 5:
V = 4/3 x π x 125 = 166.6 cubic cm
for radius 6:
V = 4/3 x π x 216 = 288 cubic cm

Question 10.
Sphere A has a radius of 9 feet. Sphere B has a diameter of 36 feet. Which of the following is a correct description of how the volumes of the spheres are related?
(A) The volumes are equal.
(B) The volume of Sphere B is 2 times
(C) The volume of Sphere B is 4 times
(D) The volume of Sphere B is 8 times
Answer: Option D is correct.
Sphere A:
radius = 9 feet
If the sphere’s radius formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
The volume of Sphere, V = (4/3)πr^3
V = 4/3 x 3.14 x 9 x 9 x 9 = 3052.08
The volume of sphere A is 3052.08 cubic feet.
Sphere B:
diameter = 36 feet
r = d/2 = 36/2 = 18 ft
V = 4/3 x 3.14 x 18 x 18 x 18
V = 24416.64 cubic ft
To know which option is correct.
first, read the options then we get to know what we have to do in the next step.
Now divide the volumes we got and let it be X.
X = 24416.64/3052.08
X = 8
Therefore, the volume of sphere B is 8 times.

Spiral Review

Question 11.
Edwin collects data on the ages of several used phones and the current value of the phones. He plots the data to make a scatter plot, with age along the x-axis and value along the y-axis. What can you predict about the slope of the trend line for Edwin’s scatter plot? Explain.
Answer:
– for one, you can find the equation for the trend line by first finding the average of each pair of points in the scatter plot.
– It is important to know that the point where the line intersects the origin is the value of the dependent variable

Question 12.
Approximate the volume of the cone shown here. Use 3.14 for π and round the volume to the nearest tenth.

Answer:
The given dimensions are:
height = 6m
radius = 3.4 m
The volume of the cone = 1/3πr^2h
V = 1/3 x 3.14 x 3.4 x 3.4 x 6
V = 1/3 x 217.7904
V = 72.5968
The nearest tenth value is 72.6
Therefore, the volume of the sphere is 72.6 cubic mts

Question 13.
A triangle has sides of length 3 inches, 5 inches, and 6 inches. Is the triangle a right triangle? Explain how you know.
Answer:
by Pythagoras theorem,
a^2 + b^2 = c^2
a = 3; b = 5; c = 6
a + b > c
3 + 5 > 6
8 > 6
b + c > a
5 + 6 > 3
11 > 3
c + a > b
6 + 3 > 5
9 > 5
yes, it forms a right triangle.