Suppose the altitude of a solid right prism is expanded by 60% while maintaining a constant base area. By what percentage will the total volume of the prism increase?

Correct Answer: 60%

To find the percentage increase in the total volume of the prism, let us use the formula for the volume of a right prism.

The volume of a solid right prism is given by:

$V=A\times h$

where:
$V$ = original volume
$A$ = base area of the prism
$h$ = original altitude (height) of the prism

According to the problem statement, the base area $A$ remains constant, while the altitude $h$ is expanded by 60%.

The new altitude $h^{\prime }$ can be expressed as:

$h^{\prime }=h+0.60h=1.60h$

Now, let us calculate the new volume $V^{\prime }$:

$V^{\prime }=A\times h^{\prime }=A\times \left(1.60h\right)=1.60(A\times h)=1.60V$

To calculate the percentage increase in volume, we use the percentage change formula:

$\text{Percentage Increase}=\frac{V^{\prime }-V}{V}\times 100\%$

Substituting $V^{\prime }=1.60V$ into the equation:

$\text{Percentage Increase}=\frac{1.60V-V}{V}\times 100\%=\frac{0.60V}{V}\times 100\%=60\%$

Thus, the total volume of the prism increases by 60%.