Exercise 13 Page 459

We are told that the volume of a cube is

125

cubic inches. We want to find the length of its sides. Let's visualize the situation by drawing a cube and letting

s

be the length of its sides.

To calculate the surface area of a prism, we can use the following formula.

S = 2 (ℓ w + ℓ h + w h)

The terms inside the parentheses represents the area of one of the three possibly different-sized faces. Each term is multiplied by

2

because opposite faces in a rectangular prism have equal dimensions. In our case, all the dimensions have the same length

s

because our prism is a cube.

S = 2 (s^{2} + s^{2} + s^{2}) \to S = 6 s^{2}

This is the formula for the surface area of a cube. Since

s = 5,

let's substitute this value into our new formula to calculate

S .

10.1.1 Cube Roots p.459

10.1.2 Surface Area and Volume of a Cylinder p.463-464

10.1.3 Volumes of Cones and Pyramids p.468-469

10.1.4 Volume of a Sphere p.472-473

10.1.5 Applications of Volume p.476