Question

Question in the screenshot

Answer 1

The area of any given circle can be found with the following formula;

• 
  `A=\pi r^2`

The letter
`r` in this formula represents the radius of the given circle.

The figure shows one full circle and one half circle.

The colored area represents the difference of the area of the half circle from the area of the full circle.

Therefore, our mission is to subtract the area of the full circle from half the area of the half circle.

First, let's find the area of the semicircle. If its diameter is
`24` millimeters, its radius must be
`12` millimeters.

• 
  `A_(half)=(\pi r^2)/(2) =(\pi (12mm)^2)/(2)=(72\pi)mm^2`

Similarly, the diameter of the full circle inside is the radius of the half circle. This is because the full circle fits inside the half circle and is tangent to it.

• 
  `A_(full)=\pi r^2=\pi (6mm)^2=(36\pi)mm^2`

The difference of these two numbers will give us the shaded area.

• 
  `(72\pi )mm^2-(36\pi )mm^2=(36\pi )mm^2`

Answer:
`36\pi`

Unit:
`mm^2`