What is the average area of a circle with a 240 mm diameter?

What is the average area of a circle with a 240 mm diameter?

• A. 452.16 cm2
• B. 1,808.64 cm2
• C. 150.72 cm2
• D. 75.36 cm2

Answer: (A)

To find the average area of a circle given its diameter, you start by calculating the radius. The radius is half of the diameter, so for a circle with a 240 mm diameter, the radius would be 120 mm. Next, you use the formula for the area of a circle, which is given by: \[ \text{Area} = \pi r^2 \] Substituting the radius into the formula: \[ \text{Area} = \pi (120 \text{ mm})^2 \] \[ \text{Area} = \pi (14,400 \text{ mm}^2) \] \[ \text{Area} \approx 3.14 \times 14,400 \text{ mm}^2 \] \[ \text{Area} \approx 45,216 \text{ mm}^2 \] Since area is often expressed in square centimeters (cm²) in practical applications, you convert this measurement from mm² to cm². Knowing that 1 cm² equals 100 mm²: \[ \text{Area} = \frac{45,216 \text{ mm}^2}{100} = 452.16 \text{ cm

To find the average area of a circle given its diameter, you start by calculating the radius. The radius is half of the diameter, so for a circle with a 240 mm diameter, the radius would be 120 mm.

Next, you use the formula for the area of a circle, which is given by:

[ \text{Area} = \pi r^2 ]

Substituting the radius into the formula:

[ \text{Area} = \pi (120 \text{ mm})^2 ]

[ \text{Area} = \pi (14,400 \text{ mm}^2) ]

[ \text{Area} \approx 3.14 \times 14,400 \text{ mm}^2 ]

[ \text{Area} \approx 45,216 \text{ mm}^2 ]

Since area is often expressed in square centimeters (cm²) in practical applications, you convert this measurement from mm² to cm². Knowing that 1 cm² equals 100 mm²:

[ \text{Area} = \frac{45,216 \text{ mm}^2}{100} = 452.16 \text{ cm