Question

a circular table is painted yellow with a red square in the middle. the radious 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.

Answer 1

To find the area of the yellow part of the tabletop, subtract the area of the red square (9x²) from the area of the circular tabletop (36πx²), which gives (36π - 9)x².

Step-by-step explanation:

To calculate the area of the yellow part of the tabletop, we need to find the area of the total tabletop (a circle) and subtract the area of the red square in the middle. The radius of the circular tabletop is given as 6x, so the area of the circle (Acircle) is A = πr² = π(6x)² = 36πx². The side length of the red square is 3x, so the area of the square (Asquare) is A = (3x)² = 9x². Now, we subtract the area of the square from the area of the circle to find the yellow area (Ayellow):

Ayellow = Acircle - Asquare = 36πx² - 9x² = (36π - 9)x². This formula represents the area of the yellow part of the tabletop.

Answer 2

Area of yellow is (area of circle) - (area of square)
Area of yellow is π(6x)2 - (3x)2
Area of yellow is 36x2π - 9x2
Area of yellow is 9x2(4π - 1)