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garik1379 [7]
3 years ago
6

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

Mathematics
1 answer:
DerKrebs [107]3 years ago
7 0

Answer:

  • Area of the circle is 56.25π square feet.

Step-by-step explanation:

<u>Given that</u>:

  • The circumference of a circle is 15π ft.

<u>To Find</u>:

  • What is the area, in square feet?

<u>We know that</u>:

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

Where,

  • Radius is denoted as R.

<u>Finding the radius of the circle</u>:

Circumference of a circle = 15π

⟶ 2πR = 15π

⟶ 2πR = 2π × 7.5

Cancelling 2π.

⟶ R = 7.5

∴ Radius of the circle = 7.5 ft.

<u>Finding the area of the circle</u>:

⟶ 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

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