Circumference and Area of Circles Test Answer Key with Scoring – Grade 7

Question 1 Circumference and radius (2 points)

1. r = 22 ÷ 2 = 11 cm
2. C = πd = 22π cm

Scoring: 1 point for each part.

Question 2 Area of a circle (2 points)

A = 3.14 × 15² = 3.14 × 225 = 706.5.

A = 706.5 in²

Scoring: 1 point for substituting correctly, 1 point for the answer with units.

Question 3 Area from the circumference (3 points)

d = 50.24 ÷ 3.14 = 16 m. r = 8 m. A = 3.14 × 8² = 3.14 × 64 = 200.96.

d = 16 m, r = 8 m, A = 200.96 m²

Scoring: 1 point for the diameter, 1 point for the radius, 1 point for the area.

Question 4 Semicircle (2 points)

1. r = 10. Half of 3.14 × 100 = 314 ÷ 2 = 157 cm²
2. Curved edge: 3.14 × 20 ÷ 2 = 31.4. Add the 20 cm diameter: 51.4 cm

Scoring: 1 point for each part.

Question 5 Explain the area formula (3 points)

1. b = half of 2π × 6 = 6π in
2. h equals the radius: 6 in
3. Area = b × h = 6π × 6 = 36π in², the same as πr² = π × 6².

Scoring: 1 point for each part.

Question 6 Wheel distance (2 points)

One turn: 3.14 × 20 = 62.8 in. 300 turns: 62.8 × 300 = 18,840 in. 18,840 ÷ 12 = 1,570.

1,570 ft

Scoring: 1 point for the distance in inches, 1 point for converting to feet.

Question 7 Flower bed (3 points)

1. Full circle: 3.14 × 12² = 452.16. One fourth: 452.16 ÷ 4 = 113.04 m²
2. Square: 12 × 12 = 144. 144 − 113.04 = 30.96 m²

Scoring: part a, 1 point for the full-circle area and 1 point for dividing by 4; part b, 1 point.

Question 8 Compare two circles (3 points)

1. A: 2π × 5 = 10π ft. B: 2π × 10 = 20π ft.
2. A: π × 25 = 25π ft². B: π × 100 = 100π ft².
3. 100π ÷ 25π = 4, so the area of B is 4 times the area of A.

Scoring: 1 point for each part.