a circular table is painted yellow with a red square in the middle the radius of the tabletop is 6x the side legh of the red square is 3x what is the area of the yellow part of the tabletop. write answer in factored form
To find the area of the yellow part of the tabletop, we need to first find the area of the entire tabletop and then subtract the area of the red square.
Let's start by finding the area of the entire tabletop, which is a circle. The formula to find the area of a circle is A = πr^2, where A is the area and r is the radius.
Given that the radius of the tabletop is 6x, we can substitute this value into the formula:
A = π(6x)^2
A = π(36x^2)
A = 36πx^2
Next, let's find the area of the red square. The area of a square is given by the formula A = s^2, where A is the area and s is the side length.
Given that the side length of the red square is 3x, we can substitute this value into the formula:
A = (3x)^2
A = 9x^2
Now, we can find the area of the yellow part by subtracting the area of the red square from the area of the entire tabletop:
Area of yellow part = Area of tabletop - Area of red square
Area of yellow part = 36πx^2 - 9x^2
To write the answer in factored form, we can factor out the common term x^2:
Area of yellow part = x^2(36π - 9)
Therefore, the area of the yellow part of the tabletop is x^2(36π - 9) in factored form.