Question

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

• A. 1468.4 cu cm
  
• B. 2008.6 cu cm
  
• C. 2438.7 cu cm
  
• D. 2478.7 cu cm
  

Answer 1

The correct option is C 2438.7 cu cm


Length of the side of the triangular base(s) = 16 cm
Therefore, the perimeter of the base$=s+s+s=16+16+16=48$ cm
Let the length of the prism be $l$.
We know that the lateral surface area = perimeter of the base × length of the prism
$\Rightarrow 1056=48\times l$
$l=$$\frac{1056}{48}$$=22$ cm
Now, volume = area of base $\times$ length of the prism
Area of the base $=\frac{\sqrt{3}}{4}\times s^2=\frac{\sqrt{3}}{4}\times {16}^2=110.85$ sq cm

Therefore, the volume of the prism $=110.85\times 22=2438.7$ cu cm