Question

I need help please!!
A circular picture of circumference 88 cm is mounted on a circular cardboard, leaving a margin of 7 cm all around. Find the area of the margin.

Answer 1

A=πr^2
C=2πr
Picture Circumference = 2πr = 88 cm
Find the Radius
r=88/2π

The frame's margin is 7 cm. Which means that the radius is 7cm larger than that of the picture.

rmargin = rpicture + 7
The area of a circle is πr^2

We know that the area of the margin is the desired value. If looking at the picture and the picture frame it is a circle placed on top of another circle. Thus the area of the margin minus the area of the picture will give the area of the margin itself.

Putting it all together
A = Amargin - Apicture
A=π〖rmargin〗^()2-π〖rpicture〗^2
A= π〖rpicture+7〗^2 - π〖rpicture〗^2
A= π〖88/2π+7〗^2 - π〖88/2π〗^2
A= 〖88+14π)/2〗^2- 〖88/2〗^2

I attached a word doc that has a better visualization of the formulas.