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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

Chapter Test

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Exercise 11 Page 755

Use the formulas for the volume and surface area of a prism.

Volume: 220 cm^3
Surface Area: 238cm^2

Practice makes perfect

Consider the given 3-D figure.

We identify this solid as a prism. Let's first calculate the volume and then the surface area.

Volume

The volume of a rectangular prism with length l, width w, and height h can be calculated using the formula below. V=l wh We are given that l= 11, w= 5, and h= 4, so we have enough information to calculate the value of V.

V=l wh

SubstituteValues

Substitute values

V=( 11)( 5)( 4)

Multiply

V=220

The volume of the prism is 220 cm^3.

Surface area

To calculate the surface area of a rectangular prism, we can use the formula below. 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 we used above, so we will substitute them into the formula to calculate S.

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

SubstituteValues

Substitute values

S=2( 11* 5+ 11* 4+ 5* 4)

▼

Evaluate right-hand side

Multiply

S=2(55+44+20)

Add terms

S=2(119)

Multiply

S=238

The surface area is 238cm^2.