Question

The lateral surface area of this prism is $1056$ cm${}^2$. Find its volume.

• A. $24386.56$ cm${}^3$
• B. $243.8656$ cm${}^3$
• C. $2438.656$ cm${}^3$
• D. None of the above

Answer 1

The correct option is C $2438.656$ cm${}^3$

Length of a side of the triangular base $s=16$ cm
$\therefore$ Perimeter of the base $=s+s+s=16+16+16=48$ cm

We know, lateral surface area $=$ perimeter of base $\times$ length of the prism
$⟹1056=48\times$ length of prism
$⟹$ length of prism $=\frac{1056}{48}=22$ cm

Now, Volume $=$ area of base $\times$ length of the prism
Area of base $=\frac{\sqrt[2]{23}}{4}{s}^2$

$=\frac{\sqrt[2]{23}}{4}\times {16}^2$

$=\frac{1.732}{4}\times 256$

$=1.732\times 64=110.848$ cm${}^2$

$\therefore$ Volume of the prism $=110.848\times 22=2438.656$ cm${}^3$

Option (c.) is correct.