This handy Spectrum Math Grade 7 Answer Key Chapter 5 Lesson 5.5 Circles: Circumference provides detailed answers for the workbook questions
Spectrum Math Grade 7 Chapter 5 Lesson 5.5 Circles: Circumference Answers Key
A circle is a set of infinite points that are all the same distance from a given point, called the center. The perimeter of a circle is called the circumference. The diameter is a segment that passes through the center of the circle and has both endpoints on the circle. The radius is a segment that has as its endpoints the circle and the center. The relationship between the circumference (C) and the diameter [d] is C ÷ d = π. Pi (π) is approximately 3\(\frac{1}{7}\) or 3.1 4. To find the circumference, diameter, or radius of a circle, use the formulas C = π × d or C = 2 × π × r.
Complete the table. Use 3.1 4 for π.
Question 1.
a. Diameter: ___________ feet
b. Radius: _____________ feet
c. Circumference: 4.71 feet
Answer:
a. Diameter: 1.5 feet
b. Radius: 0.75 feet
Explanation:
Given,
Circumference: 4.71 feet, π = 3.14
C = π × d
4.71 = 3.14 x d
d = 4.71 ÷ 3.14
d = 1.5 ft.
C = 2 × π × r.
4.71 = 2 x 3.14 x r
4.71 = 6.28 r
r = 4.71 ÷ 6.28
r = 0.75 ft.
Question 2.
a. Diameter: 3.5 meters
b. Radius: ___________ meters
c. Circumference: ___________ meters
Answer:
b. Radius: 1.75 meters
c. Circumference: 10.99 meters.
Explanation:
Given,
Diameter: 3.5 meters, π = 3.14
C = π × d
C = 3.14 x 3.5
C = 10.99 meters.
Radius = d/2
r = 3.5 ÷ 2
r = 1.75 meters.
Question 3.
a. Diameter: ___________ inches
b. Radius: 3.25 inches
c. Circumference: ___________ inches
Answer:
a. Diameter: 6.5 inches
c. Circumference: 20.41 inches.
Explanation:
Given,
Radius: 3.25 inches, π = 3.14
Diameter = 2r
D = 2 x 3.25
D = 6.5 inches.
C = π × d
C = 3.14 x 6.5
C = 20.41 inches.
Question 4.
a. Diameter: ___________ yards
b. Radius: ___________ yards
c. Circumference: 26.69 yards
Answer:
a. Diameter: 8.5 yards
b. Radius: 4.25 yards.
Explanation:
Given,
Circumference: 26.69 yd, π = 3.14
C = π × d
26.69 = 3.14 x d
d = 26.69 ÷ 3.14
d = 8.5 yd.
Radius = d/2
r = 8.5/2
r = 4.25 yd.
Question 5.
a. Diameter: 7.5 centimeters
b. Radius: ___________ centimeters
c. Circumference: ___________ centimeters
Answer:
b. Radius: 3.75 centimeters
c. Circumference: 23.55 centimeters.
Explanation:
Given,
Diameter: 7.5 centimeters, π = 3.14
Radius = d/2
r = 7.5/2
r = 3.75 cm.
C = π × d
C = 3.14 x 7.5
C = 23.55 cm.
Question 6.
a. Diameter: ___________ inches
b. Radius: 15 inches
c. Circumference: ___________ inches
Answer:
a. Diameter: 30 inches
c. Circumference: 94.2 inches.
Explanation:
Given,
Radius: 15 inches, π = 3.14
Diameter = 2r
D = 2 x 15
D = 30 inches.
C = π × d
C = 3.14 x 30
C = 94.2 inches.
Question 7.
a. Diameter: ___________ meters
b. Radius: ___________ meters
c. Circumference: 7.85 meters
Answer:
a. Diameter: 2.5 meters
b. Radius: 1.25 meters.
Explanation:
Given,
Circumference: 7.85 meters, π = 3.14
C = π × d
7.85 = 3.14 x d
D = 7.85 ÷ 3.14
D = 2.5 m.
Radius = d/2
r = 2.5/2
r = 1.25 m.
Question 8.
a. Diameter: 5 kilometers
b. Radius: ___________ kilometers
c. Circumference: ___________ kilometers
Answer:
b. Radius: 2.5 kilometers
c. Circumference: 15.7 kilometers
Explanation:
Given,
Diameter: 5 kilometers, π = 3.14
Radius = d/r
r = 5/2
r = 2.5 km.
C = π × d
C = 3.14 x 5
C = 15.7 km.
Question 9.
a. Diameter: ___________ feet
b. Radius: ___________ feet
c. Circumference: 31.4 feet
Answer:
a. Diameter: 10 feet
b. Radius: 5 feet
Explanation:
Given,
Circumference: 31.4 feet, π = 3.14
C = π × d
31.4 = 3.14 x d
d = 31.4 ÷ 3.14
d = 10 ft.
Radius = d/2
r = 10/2
r = 5 ft.
Question 10.
a. Diameter: ___________ centimeters
b. Radius: 45 centimeters
c. Circumference: ___________ centimeters
Answer:
a. Diameter: 90 centimeters
c. Circumference: 282.6 centimeters.
Explanation:
Given,
Radius: 45 centimeters, π = 3.14
Diameter = 2r
D = 2 x 45
D = 90 cm.
C = π × d
C = 3.14 x 90
C = 282.6 cm.
Question 11.
a. Diameter: 4 yards
b. Radius: ___________ yards
c. Circumference: ___________ yards
Answer:
b. Radius: 2 yards
c. Circumference: 12.56 yards.
Explanation:
Given,
Diameter: 4 yards, π = 3.14
Radius = d/2
r = 4/2
r = 2 yd.
C = π × d
C = 3.14 x 4
C = 12.56 yd.
Question 12.
a. Diameter: ___________ miles
b. Radius: ___________ miles
c. Circumference: 9.42 miles
Answer:
a. Diameter: 3 miles
b. Radius: 1.5 miles
Explanation:
Given,
Circumference: 9.42 miles, π = 3.14
C = π × d
9.42 = 3.14 x d
d = 9.42 ÷ 3.14
d = 3 miles.
Radius = d/2
r = 3/2
r = 1.5 miles.
Complete the chart for each circle described below. Use 3.14 for π . When necessary, round to the nearest hundredth.
Question 1.
a. Radius: 2 m
b. Diameter: ___________ m
c. Circumference: ___________ m
Answer:
b. Diameter: 4 m
c. Circumference: 12.56 m
Explanation:
Given,
Radius: 2 m, π = 3.14
Diameter = 2r
D = 2 x 2
D = 4 m
C = π x d
C = 3.14 x 4
C = 12.56 m
Question 2.
a. Radius: ___________ cm
b. Diameter: 18 cm
c. Circumference: ___________ cm
Answer:
a. Radius: 9 cm
c. Circumference: 56.52 cm
Explanation:
Given,
Diameter: 18 cm, π = 3.14
Radius = d/2
r = 18/2
r = 9 cm.
C = π x d
C = 3.14 x 18
C = 56.52 cm.
Question 3.
a. Radius: ___________ mm
b. Diameter: 9.2 mm
c. Circumference: ___________ mm
Answer:
a. Radius: 4.6 mm
c. Circumference: 28.89 mm
Explanation:
Given,
Diameter: 9.2 mm, π = 3.14
Radius = d/2
r = 9.2/2
r = 4.6 mm.
C = π x d
C = 3.14 x 9.2
C = 28.888 or 28.89 mm.
Question 4.
a. Radius: 5.5 in.
b. Diameter: ___________ in.
c. Circumference: ___________ in.
Answer:
b. Diameter: 11 in.
c. Circumference: 34.54 in.
Explanation:
Given,
Radius: 5.5 in, π = 3.14
Diameter = 2r
D = 2 x 5.5
D = 11 in.
C = π x d
C = 3.14 x 11
C = 34.54 in.
Question 5.
a. Radius: 12.2 cm
b. Diameter: ___________ cm
c. Circumference: ___________ cm
Answer:
b. Diameter: 24.4 cm
c. Circumference: 76.62 cm
Explanation:
Given,
Radius: 12.2 cm, π = 3.14
Diameter = 2r
D = 2 x 12.2
D = 24.4 cm
C = π x d
C = 3.14 x 24.4
C = 76.616 or 76.62 cm
Question 6.
a. Radius: ___________ ft.
b. Diameter: 5 ft.
c. Circumference: ___________ ft.
Answer:
a. Radius: 2.5 ft.
c. Circumference: 15.7 ft.
Explanation:
Given,
Diameter: 5 ft, π = 3.14
Radius = d/2
r = 5/2
r = 2.5 ft.
C = π x d
C = 3.14 x 5
C = 15.7 ft.
Question 7.
a. Radius: 17 mm
b. Diameter: ___________ mm
c. Circumference: ___________ mm
Answer:
b. Diameter: 34 mm
c. Circumference: 106.76 mm
Explanation:
Given,
Radius: 17 mm, π = 3.14
Diameter = 2r
D = 2 x 17
D = 34 mm
C = π x d
C = 3.14 x 17
C = 106.76 mm.
Question 8.
a. Radius: 3\(\frac{1}{2}\) ft.
b. Diameter: ___________ ft.
c. Circumference: ___________ ft.
Answer:
b. Diameter: 7 ft.
c. Circumference: 21.98 ft.
Explanation:
Given,
Radius: 3\(\frac{1}{2}\) ft, π = 3.14
Diameter = 2r
D = 2 x 3\(\frac{1}{2}\) ft.
D = 2 x \(\frac{7}{2}\) ft.
D = 7 ft.
C = π x d
C = 3.14 x 7
C = 21.98 ft.
Question 9.
a. Radius: ___________ cm
b. Diameter: 13 cm
c. Circumference: ___________ cm
Answer:
a. Radius: 6.5 cm
c. Circumference: 40.82 cm
Explanation:
Given,
Diameter: 13 cm, π = 3.14
Radius = d/2
r = 13/2
r = 6.5 cm.
C = π x d
C = 3.14 x 13
C = 40.82 cm.
Question 10.
a. Radius: ___________ yd.
b. Diameter: 3.8 yd.
c. Circumference: ___________ yd.
Answer:
a. Radius: 1.9 yd.
c. Circumference: 11.93 yd.
Explanation:
Given,
Diameter: 3.8 yd, π = 3.14
Radius = d/2
r = 3.8/2
r = 1.9 yd.
C = π x d
C = 3.14 x 3.8
C = 11.93 yd.
Question 11.
a. Radius: 3 cm
b. Diameter: ___________ cm
c. Circumference: ___________ cm
Answer:
b. Diameter: 6 cm
c. Circumference: 18.84 cm.
Explanation:
Given,
Radius: 3 cm, π = 3.14
Diameter = 2r
D = 2 x 3
D = 6 cm
C = π x d
C = 3.14 x 6
C = 18.84 cm.
Question 12.
a. Radius: ___________ m
b. Diameter: 7 m
c. Circumference: ___________ m
Answer:
a. Radius: 3.5 m
c. Circumference: 21.98 m.
Explanation:
Given,
Diameter: 7 m, π = 3.14
Radius = d/2
r = 7/2
r = 3.14 m.
C = π x d
C = 3.14 x 7
C = 21.98 m.
Question 13.
a. Radius: ___________ km
b. Diameter: 4 km
c. Circumference: ___________ km
Answer:
a. Radius: 2 km
c. Circumference: 12.56 km.
Explanation:
Given,
Diameter: 4 km, π = 3.14
Radius = d/2
r = 4/2
r = 2 km.
C = π x d
C = 3.14 x 4
C = 12.56 km.
Question 14.
a. Radius: 4.5 in.
b. Diameter: ___________ in.
c. Circumference: ___________ in.
Answer:
b. Diameter: 9 in.
c. Circumference: 28.26 in.
Explanation:
Given,
Radius: 4.5 in., π = 3.14
Diameter = 2r
D = 2 x 4.5
D = 9 in.
C = π x d
C = 3.14 x 9
C = 28.26 in.
Question 15.
a. Radius: 5.6 mm
b. Diameter: ___________ mm
c. Circumference: ___________ mm
Answer:
b. Diameter: 11.2 mm
c. Circumference: 35.17 mm.
Explanation:
Given,
Radius: 5.6 mm, π = 3.14
Diameter = 2r
D = 2 x 5.6
D = 11.2 mm
C = π x d
C = 3.14 x 11.2
C = 35.17 mm.
Find the circumference for each circle below. Use 3.14 for π. When necessary, round to the nearest hundredth.
Question 1.
a.
_____________ m
Answer:
18.84 m.
Explanation:
Given,
Radius: 3 m, π = 3.14
Diameter = 2r
D = 2 x 3
D = 6 m.
C = π x d
C = 3.14 x 6
C = 18.84 m.
b.
_____________ cm
Answer:
15.7 cm.
Explanation:
Given,
Diameter = 5 cm, π = 3.14
C = π x d
C = 3.14 x 5
C = 15.7 cm.
c.
___________ in.
Answer:
46.47 in.
Explanation:
Given,
Radius: 7.4 in, π = 3.14
Diameter = 2r
D = 2 x 7.4
D = 14.8 in.
C = π x d
C = 3.14 x 14.8
C = 46.47 in.
Question 2.
a.
_____________ km
Answer:
1.57 km.
Explanation:
Given,
Diameter: 0.5 km, π = 3.14
C = π x d
C = 3.14 x 0.5
C = 1.57 km.
b.
_____________ ft.
Answer:
69.08 ft.
Explanation:
Given,
Radius: 11 ft, π = 3.14
Diameter = 2r
D = 2 x 11
D = 22 ft.
C = π x d
C = 3.14 x 22
C = 69.08 ft.
c.
_____________ m
Answer:
32.03 m.
Explanation:
Given,
Radius: 5.1 m, π = 3.14
Diameter = 2r
D = 2 x 5.1
D = 10.2 m.
C = π x d
C = 3.14 x 10.2
C = 32.028 or 32.03 m.
Question 3.
a.
_____________ yd.
Answer:
144.44 yd.
Explanation:
Given,
Radius: 23 yd, π = 3.14
Diameter = 2r
D = 2 x 23
D = 46 yd.
C = π x d
C = 3.14 x 46
C = 144.44 yd.
b.
_____________ cm
Answer:
20.41 cm.
Explanation:
Given,
Diameter: 6.5 cm, π = 3.14
C = π x d
C = 3.14 x 6.5
C = 20.41 cm.
c.
_____________ mm
Answer:
131.88 mm.
Explanation:
Given,
Diameter: 42 mm, π = 3.14
C = π x d
C = 3.14 x 42
C = 131.88 mm.
Question 4.
a.
_____________ m
Answer:
13.50 m.
Explanation:
Given,
Diameter: 4.3 m, π = 3.14
C = π x d
C = 3.14 x 4.3
C = 13.502 or 13.50 m.
b.
_____________ cm
Answer:
81.64 cm.
Explanation:
Given,
Radius: 13 cm, π = 3.14
Diameter = 2r
D = 2 x 13
D = 26 cm.
C = π x d
C = 3.14 x 26
C = 81.64 cm.
c.
_____________ in.
Answer:
125.6 in.
Explanation:
Given,
Radius: 20 in., π = 3.14
Diameter = 2r
D = 2 x 20
D = 40 in.
C = π x d
C = 3.14 x 40
C = 125.6 in.
Question 5.
a.
_____________ cm
Answer:
3.93 cm.
Explanation:
Given,
Diameter: 1.25 cm, π = 3.14
C = π x d
C = 3.14 x 1.25
C = 3.925 or 3.93 cm.
b.
_____________ in.
Answer:
219.8 in.
Explanation:
Given,
Radius: 35 in, π = 3.14
Diameter = 2r
D = 2 x 35
D = 70 in.
C = π x d
C = 3.14 x 70
C = 219.8 in.
c.
_____________ ft.
Answer:
2.20 ft.
Explanation:
Given,
Diameter: 0.7 ft, π = 3.14
C = π x d
C = 3.14 x 0.7
C = 2.198 or 2.20 ft.
Question 6.
a.
_____________ mi.
Answer:
0.06 mi.
Explanation:
Given,
Radius: 0.01 mi, π = 3.14
Diameter = 2r
D = 2 x 0.01
D = 0.02 mi.
C = π x d
C = 3.14 x 0.02
C = 0.0628 or 0.06 mi.
b.
_____________ yd.
Answer:
6.28 yd.
Explanation:
Given,
Diameter: 2 yd, π = 3.14
C = π x d
C = 3.14 x 2
C = 6.28 yd.
c.
_____________ m
Answer:
79.25 m.
Explanation:
Given,
Diameter: 25.24 m, π = 3.14
C = π x d
C = 3.14 x 25.24
C = 79.25 m.