Circles and compound shapes -Circumference and Area Challenges

Determine the diameter of a circle that has a radius of 5 feet.

• 8 feet

• 12 feet

• 15 feet

• 10 feet

Answer explanation

The diameter of a circle is twice the radius. Given a radius of 5 feet, the diameter is 5 feet x 2 = 10 feet. Therefore, the correct answer is 10 feet.

If the diameter of a circle is 12 inches, what is its radius?

• 6 inches

• 10 inches

• 8 inches

• 4 inches

Answer explanation

The radius of a circle is half of its diameter. Given the diameter is 12 inches, the radius is 12 inches ÷ 2 = 6 inches. Therefore, the correct answer is 6 inches.

What is the circumference of a circle with a radius of 7 cm?

• 50.24 cm

• 28.00 cm

• 43.98 cm

• 21.99 cm

Answer explanation

The circumference of a circle is calculated using the formula C = 2πr. For a radius of 7 cm, C = 2 × π × 7 ≈ 43.98 cm. Thus, the correct answer is 43.98 cm.

Calculate the area of a circle with a diameter of 10 m.

• 100 m²

• 50.24 m²

• 78.54 m²

• 31.42 m²

Answer explanation

To find the area of a circle, use the formula A = πr². The radius is half the diameter, so r = 5 m. Thus, A = π(5)² = 25π ≈ 78.54 m². Therefore, the correct answer is 78.54 m².

What is the circumference of a circle with a diameter of 8 cm?

• 25.12 cm

• 30.16 cm

• 20 cm

• 15.7 cm

Answer explanation

The circumference of a circle is calculated using the formula C = πd. For a diameter of 8 cm, C = π × 8 ≈ 25.12 cm. Thus, the correct answer is 25.12 cm.

A circular garden has a radius of 3 m. What is its circumference?

• 12 m

• 6π m

• 9π m

• 3π m

Answer explanation

The circumference of a circle is calculated using the formula C = 2πr. For a radius of 3 m, C = 2π(3) = 6π m. Thus, the correct answer is 6π m.

If the radius of a circle is 6 inches, what is its area?

• 36π square inches

• 24π square inches

• 18π square inches

• 12π square inches

Answer explanation

The area of a circle is calculated using the formula A = πr². For a radius of 6 inches, A = π(6)² = π(36) = 36π square inches. Thus, the correct answer is 36π square inches.

Find the area of a semicircle with a radius of 4 cm.

• 8π cm²

• 12π cm²

• 16π cm²

• 4π cm²

Answer explanation

The area of a semicircle is given by the formula (1/2)πr². For a radius of 4 cm, the area is (1/2)π(4)² = (1/2)π(16) = 8π cm². Thus, the correct answer is 8π cm².

Calculate the area of a compound shape made of a rectangle (length 10 m, width 4 m) and a semicircle on one of the shorter sides.

• 46.28 m²

• 30 m²

• 40 m²

• 52.5 m²

Answer explanation

The area of the rectangle is 10 m * 4 m = 40 m². The radius of the semicircle is 2 m (half the width). The area of the semicircle is (1/2) * π * (2 m)² ≈ 6.28 m². Total area = 40 m² + 6.28 m² = 46.28 m².

A circular pool has a diameter of 20 feet. What is the area of the pool?

• 80π square feet

• 50π square feet

• 100π square feet

• 200 square feet

Answer explanation

The area of a circle is calculated using the formula A = πr². The radius is half the diameter, so r = 10 feet. Thus, A = π(10)² = 100π square feet. Therefore, the correct answer is 100π square feet.