Spectrum Math Grade 8 Chapter 5 Lesson 13 Answer Key Problem-Solving with Volume

Students can use the Spectrum Math Grade 8 Answer Key Chapter 5 Lesson 5.13 Problem-Solving with Volume as a quick guide to resolve any of their doubts.

Spectrum Math Grade 8 Chapter 5 Lesson 5.13 Problem-Solving with Volume Answers Key

Solve each problem. Use 3.14 for π. Round answers to the nearest hundredth.

Question 1.
Jermaine has a mailing cylinder for posters that measures 18 inches long and 6 inches in diameter. What volume can it hold?
The cylinder can hold ___________________ cubic inches.
Answer: The cylinder can hold 508.68 cubic inches.
Jermaine has a mailing cylinder for posters that measures 18 inches long and 6 inches in diameter.
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr2, so volume can be found using the formula: V = πr2h
The volume is expressed in cubic units, or units3.
The given values are d = 6 in. so, r = d/2 = 6/2 = 3 in. and h = 18 in.
Use 3.14 for π.
So, V = πr2h V = π(32 × 18) V = 508.68 in3
Therefore, The cylinder can hold 508.68 cubic inches.

Question 2.
An oatmeal container is a cylinder measuring 16 centimeters in diameter and 32 centimeters tall. How much oatmeal can the container hold?
The container can hold ___________________ cubic centimeters of oatmeal.
Answer:  The container can hold 6430.72 cubic centimeters of oatmeal.
An oatmeal container is a cylinder measuring 16 centimeters in diameter and 32 centimeters tall.
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr2, so volume can be found using the formula: V = πr2h
The volume is expressed in cubic units, or units3.
The given values are d = 16 cms so, r = d/2 = 16/2 =8 cms and h = 32 cms
Use 3.14 for π.
So, V = πr2h V = π(82 × 32) V = 6430.72 cms3
Therefore, The container can hold 6430.72 cubic centimeters of oatmeal.

Question 3.
Trina is using 2 glasses in an experiment. Glass A measures 8 centimeters in diameter and 18 centimeters tall. Glass B measures 10 centimeters in diameter and 13 centimeters tall. Which one can hold more liquid? How much more?
Glass ____________________ can hold ____________________ more cubic centimeters of liquid.
Answer: Glass B can hold A more cubic centimeters of liquid.
Trina is using 2 glasses in an experiment. Glass A measures 8 centimeters in diameter and 18 centimeters tall. Glass B measures 10 centimeters in diameter and 13 centimeters tall.
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr2, so volume can be found using the formula: V = πr2h
The volume is expressed in cubic units, or units3.
Volume of Glass A:
The given values are d = 8 cms so, r = d/2 = 8/2 =4 cms and h = 18 cms
Use 3.14 for π.
So, V = πr2h V = π(42 × 18) V = 904.32 cms3
Volume of Glass B:
The given values are d = 10 cms so, r = d/2 = 10/2 =5 cms and h = 13 cms
Use 3.14 for π.
So, V = πr2h V = π(52 × 13) V = 1020.5 cms3
Volume of glass B is greater than volume of glass A
Therefore, Glass B can hold A more cubic centimeters of liquid.

Question 4.
Paul completely filled a glass with water. The glass was 10 centimeters ¡n diameter and 17 centimeters tall. He drank the water. What volume of water did he drink?
Paul drank __________________ cubic centimeters of water.
Answer:  Paul drank 1334.5 cubic centimeters of water.
Paul completely filled a glass with water. The glass was 10 centimeters ¡n diameter and 17 centimeters tall. He drank the water.
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr2, so volume can be found using the formula: V = πr2h
The volume is expressed in cubic units, or units3.
The given values are d = 10 cms so, r = d/2 = 10/2 = 5 cms and h = 17 cms
Use 3.14 for π.
So, V = πr2h V = π(52 × 17) V = 1334.5 cms3
Therefore, Paul drank 1334.5 cubic centimeters of water.

Question 5.
An ice-cream cone has a height of 6 inches and a diameter of 3 inches. How much ice cream can this cone hold?
The cone can hold ___________________ cubic inches of ice cream.
Answer:  The cone can hold 14.13 cubic inches of ice cream.
An ice-cream cone has a height of 6 inches and a diameter of 3 inches.
Volume is the amount of space a three-dimensional figure occupies. The volume of a cone is calculated as \(\frac{1}{3}\)base × height.
This is because a cone occupies \(\frac{1}{3}\) of the volume of a cylinder of the same height. Base is the area of the circle, πr2.
radius = 3 / 2= 3 / 2 = 1.5 in.
height = 6 in.
V = \(\frac{1}{3}\)πr2h =  \(\frac{1}{3}\)π1.52 6 = 14.13 in.3
Therefore, The cone can hold 14.13 cubic inches of ice cream.

Question 6.
A beach ball that is 10 inches in diameter must be inflated. How much air will it take to fill the ball?
It will take _____ cubic inches of air to fill the ball.
Answer: It will take 523.33 cubic inches of air to fill the ball.
A beach ball that is 10 inches in diameter must be inflated.
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr3.
\(\frac{4}{3}\)πr3 Volume is given in cubic units or units3.
Given, d = 10 in.
The radius of a sphere is half of its diameter. Find the radius, then calculate the volume.
r = \(\frac{1}{2}\)d = \(\frac{1}{2}\)(10) = 5
V = \(\frac{4}{3}\)π(5)3 =  523.33 in3
Therefore, It will take 523.33 cubic inches of air to fill the ball.

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