Question

Henry knows that the circumference of a circle is 56.52 inches. What is the area of the circle? (Use 3.14 for  and round to the nearest hundredth)​

Answer 1

The area of circle is 254.34 square inches, if the circumference of a circle is 56.52 inches.

Explanation:

The given is,

Circumference of a circle is 56.52 inches.

`\pi =3.14`

Step:1

Formula for circumference of circle is,

`Circumference, C = 2\pi r`........................(1)

Where, r - Radius of circle

From the given,

C = 56.52 inches

Equation (1) becomes,

56.52 = 2
`\pi` (r)

56.52 = (2) (3.14) (r)

56.52 = 6.28 (r)

`r = (56.52)/(6.28)`

r = 9 inches

Step:2

Formula for area of circle,

`Area,A = \pi r^(2)`............................(2)

Where, r - Radius of circle

From the given,

r = 9 inches

Equation (2) becomes,

`A = \pi (9)^(2)`

= (3.14) (81)

= 254.34

Area of circle, A = 254.34 square inches

Result:

The area of circle is 254.34 square inches, if the circumference of a circle is 56.52 inches.