A circular table is painted yellow with a red square in the middle. The radius of the tabletop is 6x. The side length of the red square is 3x. What is the area of the yellow part of the tabletop? Write your answer in factored form.
Now I did the mirror, you can do this similarly.
To find the area of the yellow part of the tabletop, we need to subtract the area of the red square from the area of the circular table.
Step 1: Find the area of the circular table.
The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.
In this case, the radius of the table is 6x. So the area of the circular table is:
A = π(6x)^2 = 36πx^2.
Step 2: 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.
In this case, the side length of the square is 3x. So the area of the red square is:
A = (3x)^2 = 9x^2.
Step 3: Find the area of the yellow part.
To find the area of the yellow part, we need to subtract the area of the red square from the area of the circular table:
Area of yellow part = Area of circular table - Area of red square
= 36πx^2 - 9x^2
= (36π - 9)x^2
= 9(4π - 1)x^2.
So the area of the yellow part of the tabletop, in factored form, is 9(4π - 1)x^2.