Question

The circumference of a circle is 19π in. What is the area, in square inches? Express your answer in terms of π.

Answer 1

The area of circle is 90.25 π inches².

Explanation:

Given :-

Circumference of circle is 19 π in.

To Find :-

Area of circle

Solution :-

Firstly, we need to find radius of circle

Using formula

Circumference of circle = 2 π r

substitute the value

19 π inches = 2 π r

Divide each side by 2 π

19 π inches / 2 π = 2 π r / 2 π

9.5 inches = r

Now, Finding the area of circle

Using formula

Area of circle = π × r²

Where,

• r, radius of circle = 9.5 inches

Substitute the values

Area of circle = π × ( 9.5 inches)²

Evaluate the exponent

Area of circle = π × 90.25 inches ²

multiply ,we get

Area of circle = 90.25 inches²

Hence, the area of circle is 90.25 π inches².

Answer 2

A = 90.25 pi in^2

Explanation:

The circumference is given by

C = 2*pi*r

19pi = 2*pi*r

Divide each side by 2 pi

19pi / 2 pi = 2*pi*r/ 2pi

9.5 = r

The area is given by

A = pi r^2

A = pi ( 9.5)^2

A = 90.25 pi in^2