Question

A circle with radius of \greenD{3\,\text{cm}}3cmstart color #1fab54, 3, start text, c, m, end text, end color #1fab54 sits inside a circle with radius of \blueD{7\,\text{cm}}7cmstart color #11accd, 7, start text, c, m, end text, end color #11accd. What is the area of the shaded region?

Answer 1

Answer:

The area of the shaded region is 125.664 square centimetre

Step-by-step explanation:

Area of the shaded region  =  area of the circle with radius 7 cm - area of the circle with  radius 3 cm----------------(1)

Step 1:  Finding the area of the circle with radius 7 cm

Area of the circle A = $\pi r^2$

On substituting the value of the radius, we get

Area of the circle A =$\pi(7)^2$

Area of the circle A = $49 \pi$ square centimetre----------------(2)

Step 2:  Finding the area of the circle with radius 3 cm

Area of the circle a = $\pi r^2$

On substituting the value of the radius, we get

Area of the circle a  = $\pi (3)^2$

Area of the circle a  = $9 \pi$ square centimetre ----------------(3)

Step 3:  Finding the area of the shaded region

Area of the shaded region  = $49 \pi - 9\pi$

= $40 \pi$

= 125.664 square centimetre