Question

Does anybody know this?Find the area of the shaded region if PA=7 inches and PB=4 inches

Answer 1

Hi Student!

The first step that we must take before attempting to solve the problem is to gather important information. Looking at the problem we are given two lengths, PA and PB. These two lengths make up the radius of two different circles which we will need to find the area for both of them. The other important information that we must take in is that we are trying to determine the area of the shaded region.

Now that we have our important information concluded, let's move onto solving the problem. We know that we are trying to determine the area of the shaded region which means that we will need to do some subtraction between the total area of the larger circle and the total area of the smaller circle.

Area of a Circle Formula

• 
  `A=\pi*r^2`

Plug in the information

• 
  `Shaded\ Region = Larger\ Circle - Smaller\ Circle`

• 
  `Shaded\ Region = (\pi *PA^2)-(\pi*PB^2)`

• 
  `Shaded\ Region = (\pi *(7\ in)^2)-(\pi*(4\ in)^2)`

Simplify the exponents

• 
  `Shaded\ Region = (\pi *49\ in^2)-(\pi*16\ in^2)`

Subtract

• 
  `Shaded\ Region = 49\ in^2*\pi-16\ in^2*\pi`

• 
  `Shaded\ Region = 33\ in^2*\pi`

Therefore, our final answer would be that the shaded region is 33 inches squared times pi which is best described in Option D. We got this after subtracting the area of the smaller circle from the area of the larger circle which provides us with the area of the shaded region.