Exercise 19 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= 4.5, w= 4.5, and h= 4.5, so we have enough information to calculate the value of V.

V=l wh

SubstituteValues

Substitute values

V= 4.5( 4.5)( 4.5)

Multiply

Multiply

V=91.125

RoundDec

Round to 1 decimal place(s)

V ≈ 91.1

The volume of the prism is approximately 91.1 cubic meters.

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( 4.5( 4.5)+ 4.5( 4.5)+ 4.5( 4.5))

Multiply

Multiply

S=2(20.25+20.25+20.25)

AddTerms

Add terms

S=2(60.75)

Multiply

Multiply

S=121.5

The surface area is 121.5 square meters.