Question

A rectangular block has length= 4 units, width =2 units and height= 7 units. If the length, width and height are doubled, what happens to the volume?

• A. The new volume is double the original volume.
• B. The new volume is 4 times the original volume
• C. The new volume is 8 times the original volume
• D. The new volume is 6 times the original volume

Answer 1

The correct option is C

The new volume is 8 times the original volume

Given : length= 4, width =2 and height= 7

Let us find the volume for these dimensions first.

Volume $\left(V1\right)=length\times width\times height$

Volume $\left(V1\right)=4\times 2\times 7=56cubicunits$

The dimensions we get after doubling are as follows :

length= 8, width =4 and height= 14

Let us find the volume for these dimensions.

Volume $\left(V2\right)=length\times width\times height$

Volume $\left(V2\right)=8\times 4\times 14=448cubicunits$

$\frac{V2}{V1}$ = $\frac{448}{56}$ = 8

We see that $V2=8\times V1$

So, the new volume is 8 times the original volume.