Question

A rectangular prism is changed by doubling its length, halving its width, and tripling its height. How will these changes affect its volume? [Hint: draw a picture]A. The volume is multiplied by 3.B. The volume is increased by 3.C. The volume is doubled.D. The volume is multiplied by 6.

Answer 1

Let's first recall the formula for the volume of a rectangular prism:

$\text{ Volume = L x W x H}$

Where,

L = Length

W = Width

H = Height

In the given scenario, it is said that the length is doubled, width is in half and the height is tripled.

It'll be,

Length = 2L

Width = 1/2W

Height = 3H

The volume will be:

$\text{ Volume = \lparen2L\rparen\lparen}\frac{\text{ 1 }}{\text{ 2 }}\text{W\rparen\lparen3H\rparen = }\frac{\text{ 2 x 1 x 3}}{\text{ 2}}\text{ LWH}$$\text{ Volume = 3LWH = 3\lparen Original Volume\rparen}$

Therefore, the volume is multiplied by 3.

The answer is CHOICE A.