Question 1 The square has side lengths = 8. Each vertex is the center of a circle. The circles are congruent and are tangent to each other. What is the area of the shaded region (see figure below)?

-- Answer -- 64 - 16 π

There are 4 quarter circles inside the square or 1 total circle. Area = πr² = π * 4² = 16 π

Area of square = 8 * 8 = 64

Area of shaded region = 64 - 16 π

Question 2 A box in a shape of a cube has interior side lengths of 18 inches. It is used to ship a right circular cylinder with a radius of 6 inches and a height of 12 inches. What is a mathematical expression that describes the area inside the cube that isn't filled by the right circular cylinder?

-- Answer -- 18³ - (π)(6²)(12)

volume of box = 18³

volume of right circular cylinder = π r² h = (π)(6²)(12)

Volume of area inside the cube that isn't filled by the right circular cylinder = 18³ - (π)(6²)(12)