Question

The base of a prism is an equilateral triangle of perimeter 30 cm. The height of the prism is 10 cm. Find the volume of the prism.

• A. 100 $\sqrt{3}c{m}^3$
• B. 250 $\sqrt{3}c{m}^3$
• C. 200 $\sqrt{3}c{m}^3$
• D. 175 $\sqrt{3}c{m}^3$

Answer 1

The correct option is B 250 $\sqrt{3}c{m}^3$

Given that perimeter of the base triangle is 30 cm.

Let the side of the triangle be 's' cm long.

$\Rightarrow$ Perimeter of the equilateral triangle = 3s

So, $\text{/}{30}^{10}=\text{/}3s$

s = 10 cm

Now, area of the equilateral triangle

= $\frac{\sqrt{3}}{4}{s}^2=\frac{\sqrt{3}}{4}10\times 10$

= $25\sqrt{3}c{m}^2$

Volume of the prism = base area $\times$ height

= $25\sqrt{3}\times 10$

= $250\sqrt{3}c{m}^3$