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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

Practice Test

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Exercise 19 Page 875

The surface area S and the volume V of a rectangular prism with dimensions l, w, and h, are given by the formulas S=2l w +2l h+2wh and V=l w h.

Surface Area: 10x^2+18x square units
Volume: 2x^3+6x^2 cubic units

A rectangular prism has a base with side lengths l= x and w= x+3 and height h= 2x.

The surface area S and the volume V of a rectangular prism with dimensions l, w, and h, are given by the formulas S=2 l w +2 l h+2 w h and V= l w h. First, let's find the volume!

V= l w h

SubstituteExpressions

Substitute expressions

V= x ( x+3) ( 2x)

▼

Simplify right-hand side

Multiply

V=2x^2(x+3)

Distribute 2x^2

V=2x^2(x)+2x^2(3)

Multiply

V=2x^3+6x^2

Therefore, the volume of the prism is V=2x^3+6x^2 cubic units. Now, let's find the surface area of the prism.

S=2 l w +2 l h+2 w h

SubstituteExpressions

Substitute expressions

S=2( x)( x+3) +2( x)( 2x)+2( x+3)( 2x)

▼

Simplify right-hand side

Multiply

S=2x(x+3)+4x^2+4x(x+3)

Distribute x+3

S=2x^2+6x+4x^2+4x^2+12x

Add terms

S=10x^2+18x

This tells us that the surface area of the prism is S=10x^2+18x square units.