Question

A circle with radius of 3 cm\greenD{3\,\text{cm}}3cmstart color #1fab54, 3, start text, c, m, end text, end color #1fab54 sits inside a circle with radius of 11 cm\blueD{11\,\text{cm}}11cmstart color #11accd, 11, start text, c, m, end text, end color #11accd.

What is the area of the shaded region?

Round your final answer to the nearest hundredth.

Answer 1

Answer:

351.86 Square inches (to the nearest hundredth)

Step-by-step explanation:

The shaded region is referred to as the Annulus of two concentric circles.

To find the area of the shaded region is to subtract the area of the smaller circle from the area of the larger circle.

Let the radius of the larger circle=R

Let the radius of the smaller circle=r

Area of shaded region$=\pi R^2-\pi r^2= \pi(R^2- r^2)$

R=11cm, r=3cm

Therefore:

Area of shaded region

$= \pi(11^2- 3^2)\\=112\pi\\=351.86 square inches (to the nearest hundredth)$

Answer 2

Answer:

The Answer is 351.86 (Rounded to the nearest Hundredth)

Step-by-step explanation:

First, calculate the area of the whole figure, including the unshaded area which is 11cm.

The Area of a circle is πr^2 or Pi times radius squared.

π * 11cm * 11cm = 121π cm^2

Next, calculate the area of the inner figure which is 3cm

π * 3cm * 3cm = 9π cm^2

Finally, subtract the area of the inner circle from the area of the outer circle.

121π cm^2 - 9π cm^2 = 112π cm^2

≈ 351.86cm  

 

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