Question

Find the area of the shaded region in the figure below, if the diameter of the circle is 2 and the height of the rectangle is 11.

Use 3.14 for pi and round to the nearest hundredth.
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Answer 1

Answer: 20.43

Explanation:

The shape shown is a circle that overlaps a rectangle. The shaded region is a rectangle with half a circle cut out. To find the area of the shaded region, we can find the area of the rectangle and the area of the overlapping semi-circle and subtract them. The rectangle has a height of 11. The width of the rectangle is the diameter of the circle, 2. First, find the area of the rectangle:

A = length×width

A = 11⋅2

A = 22

To find the area of the circle, we need to find the radius. The radius is one half the diameter, therefore r=1. Use the value of r to solve for the area:

A = πr2

A = 3.14⋅(12)

A = 3.14

Now we can subtract half the area of the circle from the area of the rectangle:

Area of rectangle − Area of half circle = Area shaded region

22−3.14 divided by 2

A = 20.43

So the area of the shaded region is 20.43.

Answer 2

20.43

Explanation:

area of a circle is r^2 x 3.14

area of circle = 3.14

divide that by 2 because only half of the circle is cut out of the shaded region.

that would equal 1.57

to find the majority of the shaded region just multiply length x width

11 x 2 = 22

so subtract the half-circle from that

22 - 1.57 = 20.43