Question

A rectangular prism is changed by doubling its length, halving its width, and tripling its height. How will these changes affect its volume?

 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

Option A - The volume is multiplied by 3.

Explanation:

Given : A rectangular prism is changed by doubling its length, halving its width, and tripling its height.

To find : How will these changes affect its volume?

Solution :

Let L be the length, W be the width and H be the height of the rectangular prism.

The volume of the rectangular prism is
`V=L* W* H`

Now, A rectangular prism is changed by doubling its length, halving its width, and tripling its height.

i.e. L=2L ,
`W=(1)/(2)W` and H=3H

Substituting in the volume formula,

`V=2L* (1)/(2)W* 3H`

`V=3(L*W* H)`

Which means the volume is multiplied by 3.

Therefore, Option A is correct.

Answer 2

The Volume will be multiplied by 3. A.
I'm sure there is another way to go about this but I just used a test value of 2 for the length, width and height.
Then adjusted the equation and re-inserted the values and the Volume was tripled.
V=L*W*H then after adjustments
V=2L*1/2W*3H.