Question

A rectangular block has length= 6 units, width =4 units and height= 9 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= 6 units, width = 4 units and height= 9 units

Let us find the volume for these dimensions first.

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

Volume $\left(V1\right)=6\times 4\times 9=216cubicunits$

The dimensions we get after doubling are as follows :

length= 12 units, width =8 units and height= 18 units

Let us find the volume for these dimensions.

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

Volume $\left(V2\right)=12\times 8\times 18=1728cubicunits$

$\frac{V2}{V1}$ = $\frac{1728}{216}$ = 8

We see that $V2=8\times V1$

So, the new volume is 8 times the original volume