Grade 7 Math Practice Test: Circumference and Area of Circles Word Problems
- Circumference and Area of Circles: Word Problems
- 10 questions
- 15 minutes
This test applies C = πd = 2πr and A = πr² to real situations, including working backward from the circumference. Use 3.14 for π. Tip: decide first whether the question asks for the distance around (circumference) or the space inside (area).
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
A bicycle wheel has a diameter of 26 inches. How far does the bike move forward when the wheel turns once? Use 3.14 for π.
Correct answer: A
One turn rolls out the circumference: C = πd = 3.14 × 26 = 81.64 inches. 40.82 uses 13 in C = πd, and 530.66 is the area, not a distance.
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Question 2
A circular garden has a circumference of 31.4 meters. What is its radius? Use 3.14 for π.
Correct answer: A
d = C ÷ π = 31.4 ÷ 3.14 = 10 m, and the radius is half of that, 5 m. 10 m is the diameter.
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Question 3
Is one 12-inch pizza or two 8-inch pizzas more pizza? The sizes are diameters. Which is more, and by how much? Use 3.14 for π.
Correct answer: A
One 12-inch pizza: 3.14 × 6² = 113.04 sq in. Two 8-inch pizzas: 2 × 3.14 × 4² = 100.48 sq in. The difference is 12.56 sq in. Comparing diameters (12 < 16) is misleading because area depends on the square of the radius.
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Question 4
A circular coaster has a circumference of 18.84 cm. What is its area? Use 3.14 for π.
Correct answer: D
d = 18.84 ÷ 3.14 = 6 cm, so r = 3 cm and A = 3.14 × 3² = 28.26 cm². 113.04 cm² uses the diameter 6 as the radius.
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Question 5
A running track is made of two straight sides, each 100 m long, and two semicircular ends. Each semicircle has a diameter of 60 m. How long is one lap around the track? Use 3.14 for π.
Correct answer: C
The two semicircles together make one full circle with diameter 60 m: 3.14 × 60 = 188.4 m. Add the straight parts: 188.4 + 200 = 388.4 m. 294.2 m counts only one semicircle.
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Question 6
A lawn sprinkler sprays water 7 feet in every direction as it turns. What area of lawn does it water? Use 3.14 for π.
Correct answer: C
The watered region is a circle with radius 7 ft: A = 3.14 × 7² = 153.86 sq ft. 43.96 is the circumference, and 615.44 uses 14 ft as the radius.
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Question 7
A circular pool has a radius of 5 m. A path 1 m wide goes all the way around it. What is the area of the path? Use 3.14 for π.
Correct answer: D
The pool and path together form a circle with radius 6 m. Path area = 3.14 × 6² − 3.14 × 5² = 113.04 − 78.5 = 34.54 m². 113.04 m² forgets to subtract the pool.
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Question 8
The radius of a circle is doubled. What happens to its area?
Correct answer: B
Area depends on r². If r becomes 2r, the area becomes π(2r)² = 4πr². The circumference doubles, but the area becomes 4 times as large.
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Question 9
A measuring wheel has a diameter of 0.5 m. Ravi rolls it in a straight line for 157 m. How many full turns does the wheel make? Use 3.14 for π.
Correct answer: B
One turn covers C = 3.14 × 0.5 = 1.57 m, and 157 ÷ 1.57 = 100 turns. 200 uses the radius 0.25 m in C = πd.
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Question 10
A garden bed is shaped like a quarter circle with a radius of 8 feet. What is its area? Use 3.14 for π.
Correct answer: B
A full circle with radius 8 ft has area 3.14 × 64 = 200.96 sq ft, and a quarter of it is 50.24 sq ft. 100.48 sq ft would be a half circle.
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