Question

The lateral surface area of the triangular prism shown in the given image is 1056 square centimeters. Find its volume.

• A. $24386.56cucm$
• B. $243.8656cucm$
• C. $2438.656cucm$
• D. $24.38656cucm$

Answer 1

The correct option is C $2438.656cucm$

Side length of the triangular base of the prism,
$s=16cm$
Perimeter of the base of the prism $=s+s+s=16+16+16=48cm$

Lateral surface area of the triangular prism = perimeter of the base of the prism $\times$ length of the prism
$\Rightarrow 1056=48\times \text{length of the prism}$
$\Rightarrow \text{Length of the prism}=\frac{1056}{48}=22cm$

Volume of the triangular prism $=$ area of the triangular base $\times$ length of the prism
$\text{Area of the triangular base}=\frac{\sqrt{3}}{4}{s}^2$

$=\frac{\sqrt{3}}{4}\times {16}^2$
$=\frac{1.732}{4}\times 256$
$=1.732\times 64=110.848sqcm$

Volume of the triangular prism $=110.848\times 22=2438.656cucm$