Question

Three semicircles are placed in a rectangle, as shown below. The length of the rectangle is 30 m . Find the area of the shaded region. Use the value for , and do not round your answer. Be sure to include the correct unit in your answer.

Answer 1

Answer:

The area of the shaded region is: 32.25m^2

Step-by-step explanation:

Given

See attachment for rectangle and semicircles

Required

The shaded region

We have:

$l =30$ --- length of the rectangle

This means that the diameters of the three circles add up to 30m.

So, the diameter of 1 is:

$d = l/3$

$d = 30/3$

$d = 10$

The area of one circle is:

$A_1 = \pi * \frac{d^2}{8}$

$A_1 = 3.14 * \frac{10^2}{8}$

$A_1 = 3.14 * \frac{100}{8}$

$A_1 = 39.25m^2$

The area of the three circles is:

$A_2 = 3 * A_1$

$A_2 = 3 *39.25m^2$

$A_2 = 117.75m^2$

The area of the rectangle is:

$A_3 = 30 * r$

Where r is the radius of the circle

And

$r =d/2$

$r =10/2$

$r =5$

So, we have:

$A_3 = 30 * r$

$A_3 = 30 * 5$

$A_3 = 150$

So, the shaded region is:

$A_4 = A_3 - A_2$

$A_4 = 150 - 117.75$

$A_4 = 32.25m^2$