Question

The formula for the surface area of a sphere is A=4π r². A square sticker of side x is placed on a ball of radius 3x. What is the surface area of the sphere not covered by the sticker? Write your answer in factored form.

Answer 1

To find the surface area of the sphere not covered by the sticker, subtract the area of the sticker from the total surface area of the sphere.

Step-by-step explanation:

To find the surface area of the sphere not covered by the square sticker, we first need to find the surface area of the sphere and the surface area of the square sticker. The radius of the sphere is given as 3x, so the surface area of the sphere is A = 4π(3x)² = 36πx². The area of the square sticker is x². To find the surface area not covered by the sticker, we subtract the area of the sticker from the total surface area of the sphere: 36πx² - x² = (36π - 1)x².