The base of a right prism is an equilateral triangle of inradius 3 cm. Find the volume of the prism, if its height is 15cm -
Answer & explanation
Correct answer: option 3
Inradius of an equilateral triangle = \(\frac{a}{2\sqrt {3}}\)
⇒ 3 = \(\frac{a}{2\sqrt {3}}\)
⇒ a = 6\(\sqrt{3}\) cm
Area of a triangle = \(\frac{\sqrt {3}}{4}\) a2
= \(\frac{\sqrt {3}}{4}\) × 36 × 3
= 27\(\sqrt{3}\) cm2
volume of prism = area of base × height
= 27\(\sqrt{3}\) × 15 = 701.46 cm2