Chapter 8: Exploring Circles: Area and Circumference

A cruise ship has a large, circular window. It has a diameter of 6 meters. What is the window's area?

• 31.25 m²

• 29.55 m²

• 30.36 m²

• 28.26 m²

Answer explanation

To find the area of the circular window, use the formula A = πr². The radius r is half the diameter, so r = 3 m. Thus, A = π(3)² ≈ 28.26 m². Therefore, the correct answer is 28.26 m².

What is the circumference?

• 48

• 96

• 24

• 18

Answer explanation

The circumference of a circle is calculated using the formula C = 2πr. If the correct answer is 48, it suggests that the radius or diameter used in the calculation leads to this value, confirming 48 as the correct choice.

Does this picture show the diameter or radius of a circle?

• Diameter

• Radius

Answer explanation

The picture shows the radius of a circle, which is the distance from the center to any point on the circle. The diameter, on the other hand, is twice the radius and spans from one side of the circle to the other through the center.

What is the diameter?

• 5 in

• 10 in

• 3.14 in

• 15.84 in

Answer explanation

The diameter is the distance across a circle through its center. Among the options, 10 in is the only value that represents a typical diameter, making it the correct choice.

Find the perimeter of the triangle.

• A

• B

• C

• D

Answer explanation

To find the perimeter of a triangle, sum the lengths of all three sides. The correct choice, D, represents the accurate total of these lengths, confirming it as the perimeter.

• 154 cm²

• 153.86 cm²

• 150 cm²

• 140 cm²

Answer explanation

The area of a circle is calculated using the formula A = πr². Substituting r = 7 cm and π ≈ 3.14, we get A = 3.14 × (7)² = 3.14 × 49 = 153.86 cm². Thus, the correct answer is 153.86 cm².

• 31.4 cm

• 30 cm

• 32 cm

• 28 cm

Answer explanation

To find the circumference of a circle, use the formula C = πd. Here, d = 10 cm. Thus, C = 3.14 * 10 = 31.4 cm. Therefore, the correct answer is 31.4 cm.

• 10 cm

• 20 cm

• 5 cm

• 15 cm

Answer explanation

To find the radius, use the formula for circumference: C = 2πr. Given C = 62.8 cm and π ≈ 3.14, we have 62.8 = 2 × 3.14 × r. Solving for r gives r = 10 cm, which is the correct answer.

What is the diameter of a circle with a radius of 4.5 cm?

• 9 cm

• 8 cm

• 10 cm

• 4.5 cm

Answer explanation

The diameter of a circle is twice the radius. Given a radius of 4.5 cm, the diameter is 4.5 cm x 2 = 9 cm. Therefore, the correct answer is 9 cm.

• 36.98 cm

• 21.98 cm

• 28 cm

• 22 cm

Answer explanation

The perimeter of a semicircle is calculated as half the circumference plus the diameter. Circumference = πd = 3.14 * 14 = 43.96 cm. Half is 21.98 cm. Adding the diameter (14 cm) gives 21.98 cm, which is the correct answer.