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

Answer:

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

Area of a circle A = 12081.1 square inches

Step-by-step 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 $=2\pi R=2\pi (62)=124\pi =124(\frac{22}{7})=389.7 \,\,inches$

Area of a circle $=\pi r^2=\pi (62)^2=3844\pi=3844(\frac{22}{7})=12081.1$ square inches