Exercise 18 Page 71

We will start by calculating the volume of the prism before moving on to the surface area.

Volume

Let's examine the rectangular prism.

The volume of a rectangular prism with length l, width w, and height h can be calculated using the following formula. V=l wh We have been given that l= 2, w= 5, and h= 6, so we have enough information to calculate the value of V.

V=l wh

SubstituteValues

Substitute values

V= 2( 5)( 6)

Multiply

Multiply

V=60

The volume of the prism is 60 cubic inches.

Surface Area

To calculate the surface area of a rectangular prism, we can use the following formula. S=2(l w+l h+wh) The terms inside the parentheses represent the area of the three possible different sized faces. Each term is multiplied by 2 because opposite faces on a rectangular prism have equal dimensions. These are the same dimensions as used above, so we will substitute them into our new formula to calculate S.

S=2(l w+l h+wh)

SubstituteValues

Substitute values

S=2( 2( 5)+ 2( 6)+ 5( 6))

Multiply

Multiply

S=2(10+12+30)

AddTerms

Add terms

S=2(52)

Multiply

Multiply

S=104

The surface area is 104 square inches.