Question

The circumference of a circle is 15π centimeters. What is the area of the circle in terms of π?


A. 7.5π cm²

B. 15π cm²

C. 56.25π cm²

D. 225π cm²

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Answer 1

Answer:

C. 56.25π cm²

Step-by-step explanation:

The circumference of a circle is given by

C = 2 * pi *r

15 pi = 2 * pi *r

Divide each side by pi

15 = 2r

Divide by 2

15/2 = 2r/2

7.5 = r

We want to find the area

A = pi r^2

A = pi (7.5)^2

A = pi *56.25

A = 56.25 pi

Answer 2

To calculate the area of the circle in terms of pie (π) is: C. 56.25π cm².

Given the following data:

• Circumference of a circle = 15π centimeters.

To calculate the area of the circle in terms of π:

First of all, we would determine the diameter of this circle.

How to calculate the circumference of a circle.

Mathematically, the circumference of a circle is given by the formula:

$Circumference = \pi D$

Where:

• D is the diameter of a circle.

Substituting the given parameters into the formula, we have;

$15\pi = \pi D$

D = 15 centimeters.

Next, we would find the radius of this circle:

$Radius = \frac{diameter}{2} = 7.5\;centimeters.$

For the area:

$Area = \pi r^2\\ \\ Area = \pi \times 7.5^2\\ \\ Area = \pi \times 56.25$

Area = 56.25π $cm^2$

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