Question

A prism has an equilateral triangular base. The side of the triangle is 8 cm, and the height of the prism is 14 cm. The volume of the prism is cc.

• A. $204\sqrt{3}$
• B. $234\sqrt{3}$
• C. $224\sqrt{3}$

Answer 1

The correct option is C $224\sqrt{3}$

Let 's' be the side of the triangle, here s = 8 cm and height h = 14 cm

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

$\Rightarrow A=\frac{\sqrt{3}}{4}\times 8^2$

$\Rightarrow A=\frac{\sqrt{3}}{4}\times 64$

$\Rightarrow A=\sqrt{3}\times 16$

$\Rightarrow A=16\sqrt{3}c{m}^2$

$Volume=A\times h=16\sqrt{3}\times 14=224\sqrt{3}c{m}^3$