Question

What is the volume of a right prism standing on a triangular base of sides 5 cm, 5 cm and 8 cm whose lateral surface area is 828 cm² ? 

(a) 680 cm³ 

(b) 552 cm³ 

(c) 1008 cm³ 

(d) 728 cm³ 

Answer 1

(b) 552 cm³

Lateral surface area of a prism = Perimeter of base × Height 

⇒ 840 = (5 + 5 + 8) × Height 

⇒ Height = \(\frac{840}{18}\) = 46 cm.

= Semi perimeter of the triangular base = \(\frac{18}{2}\) = 9 cm

∴ Area of triangle = \(\sqrt{9(9 – 5) (9 – 5) (9 – 8)}\)     (Herons Formula)

= \(\sqrt{9\times4\times4\times1}\) = 12 cm² 

∴ Required volume of prism = Area of base × Height 

= (12 × 46) cm³ = 552cm³.