Question

The base of a prism is triangular in shape with sides $3$ cm, $4$ cm and $5$ cm. Find the volume of the prism if its height is $10$ cm.

• A. $45$ $cu.cm$
• B. $50$ $cu.cm$
• C. $60$ $cu.cm$
• D. $65$ $cu.cm$

Answer 1

Answer: (C)

$60$ $cu.cm$

Given, sides of prism are $3$ cm, $4$ cm and $5$ cm and height $=10$ cm

Let $s$ be the semi-perimeter of the triangular base of the prism.

Then $S=$ $\frac{3+4+5}{2}=6$ cm

Therefore, the area of the prism $=$ $\sqrt{s(s-a)(s-b)(s-c)}$

$=$ $\sqrt{6(6-3)(6-4)(6-5)}$

$=$ $\sqrt{6\times 3\times 2\times 1}$

$=$ $\sqrt{36}=6$ sq. cm.

Then volume of the prism $=\text{area of base}\times \text{height}$

$=$ $6\times 10$

$=$ $60$ $cu.cm$