Exercise 68 Page 672

Practice makes perfect

a The solid can be viewed as a rectangular prism with a cylinder-shaped hole in the middle. If we calculate the volume of the rectangular prism including the hole and subtract the volume of the cylinder, we obtain the volume of the solid.

The volume of the rectangular prism is the product of its width, height, and length.

V_(RP)=(5)(2)(6)=60 cm^3 The cylinder-shaped hole has a radius of 0.5 cm. With this information we can calculate the volume of the hole. V_C=π (0.5)^2(6)≈ 4.71 cm^3 Finally, we will subtract the volume of the hole from the volume of the rectangular prism (including the hole). 60 - 4.71 ≈ 55.3 cm^3

b For one example, this could be an early version of a toilet paper roll. After a few iterations, the inventor probably went with a cylindrical roll with a cylindrical hole instead of the rectangular prism version.