Question

Find the radius of a circle whose area equals the area of a rectangle that measures 2 ft. by 11 ft. (Use pi = 22/7)

Answer 1

i hope this helps you



circle area=pi.r^2


rectangle area=length. width


22/7.r^2=2.11


r^2=22.7/22

r^2=7

r=square root of 7

Answer 2

The radius of the circle is,
`√(7)` ft

Explanation:

Area of the circle(A) and Area of rectangle(A') is given by

`A = \pi r^2` .....[1]

where, r is the radius of the circle

and

A' = lw ....[2]

where, l is the length and w is the width of the rectangle.

As per the statement:

Area of circle equals the area of a rectangle.

⇒A = A'

It is also given that: a measure of rectangle is 2 ft. by 11 ft.

⇒l = 2ft and w = 11 ft

Substitute in [2] we have;

`A' = 2 * 11 = 22 ft^2`

Since, A = A'

⇒
`\pi r^2 = 22`

Use
`\pi = (22)/(7)`

then;

`(22)/(7) r^2 = 22`

Divide both sides by 22 we have;'

`(1)/(7) r^2 = 1`

Multiply both sides by 7 we have;

`r^2 = 7`

or

`r = √(7)` ft

Therefore, the radius of the circle is,
`√(7)` ft