Question

If Circle A has a radius that is five more than twice as long as the radius of circle B and the sum of the diameters of the circle is 88 inches, find the area and circumference of circle A

Answer 1

Circumference of a circle A =
`389.7 \,\,inches`

Area of a circle A = 12081.1 square inches

Explanation:

Let
`r` denotes radius of circle B.

Circle A has a radius that is five more than twice as long as the radius of circle B.

So,

Radius of circle A =
`5+2r`

Diameter of circle = 2 (radius of circle)

So,

Diameter of circle B = 2r

Diameter of circle A =
`2(5+2r)`

Sum of the diameters of the circles A and B =
`2r+2(5+2r)`

`=2r+10+4r`

`=6r+10`

As sum of the diameters of the circles is 88 inches,

`6r+10=88\\6r=78`

`r=13` inches

Radius of a circle A =
`2(5+2r)`

`=2[5+2(13)]`

`=2(5+26)`

`=2(31)`

`=62` inches

Let R denotes radius of a circle A.

R = 62 inches

Circumference of a circle
`=2\pi R=2\pi (62)=124\pi =124((22)/(7))=389.7 \,\,inches`

Area of a circle
`=\pi r^2=\pi (62)^2=3844\pi=3844((22)/(7))=12081.1` square inches