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 -

701.46 cm³

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