A rectangular prism has a volume of 15\text{ cubic centimeters}. If the length, width, and… — SAT

A rectangular prism has a volume of $15\text{ cubic centimeters}$ . If the length, width, and height of the prism are all doubled, what is the volume, in cubic centimeters, of the new rectangular prism?

A
$30$
$120$ Answer
C
$60$
D
$90$

Answer

120

The volume of a rectangular prism is proportional to the product of its length, width, and height. Doubling each of these dimensions multiplies the volume by a factor of

2 \times 2 \times 2 = 8

. Multiplying the original volume of

15\text{ cubic centimeters}

8

gives

120\text{ cubic centimeters}

Step-by-Step Solution

Identify how the volume of a rectangular prism relates to its dimensions.

The volume is given by

V = l \times w \times h

This establishes the relationship between the linear dimensions and the volume of the solid.

Determine the scale factor for the volume when all linear dimensions are doubled.

The new dimensions are

2l

2w

, and

2h

, which gives a new volume of

(2l)(2w)(2h) = 8(l \times w \times h) = 8V

. Thus, the volume scale factor is

2^3 = 8

Volume scales with the cube of the linear dimensions change.

Calculate the volume of the scaled prism using the original volume.

New Volume =

8 \times 15 = 120\text{ cubic centimeters}

Multiply the original volume by the volume scale factor to obtain the final answer.

Key Concept

Dimensional scaling of solids (volume scales cubically)

Estimated Time:45s

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