Question

The circumference of a circle is 15π ft. What is the area, in square feet? Express your answer in terms of π.

Answer 1

Answer:

• Area of the circle is 56.25π square feet.

Step-by-step explanation:

Given that:

• The circumference of a circle is 15π ft.

To Find:

• What is the area, in square feet?

We know that:

• Circumference of a circle = 2πR
• Area of a circle = πR²

Where,

• Radius is denoted as R.

Finding the radius of the circle:

Circumference of a circle = 15π

⟶ 2πR = 15π

⟶ 2πR = 2π × 7.5

Cancelling 2π.

⟶ R = 7.5

∴ Radius of the circle = 7.5 ft.

Finding the area of the circle:

⟶ Area = πR²

⟶ Area = π(7.5)²

⟶ Area = π × 7.5 × 7.5

⟶ Area = π × 56.25

⟶ Area = 56.25π

∴ Area of the circle = 56.25π ft.²