Question

The base of a prism is in the form of an equilateral triangle of perimeter 12 cm. The height of the prism is 8 cm. What is the volume of of the prism?

• A. $32\sqrt{3}c{m}^3$
  
• B. $16\sqrt{2}c{m}^3$
  
• C. $32\sqrt{2}c{m}^3$
  
• D. $16\sqrt{3}c{m}^3$

Answer 1

The correct option is A

$32\sqrt{3}c{m}^3$

Perimeter of the equilateral triangle is 12 cm

Hence each side of the equilateral triangle is $\frac{12}{3}=4cm$

Area of the triangular base = $\frac{\sqrt{3}}{4}\times (4{)}^2=\frac{\sqrt{3}}{4}\times 4\times 4$

$=4\sqrt{3}cm$

Volume of prism = $\text{Base Area}\times \text{Height}$

$=4\sqrt{3}\times 8$

$=32\sqrt{3}c{m}^3$