Question

Find the volume of a tetrahedron the sides of whose base are 9 cm, 12 cm and 15 cm and height = 15 cm.

(a) 225 cm³ 

(b) 270 cm³ 

(c) 360 cm³ 

(d) 200 cm³

Answer 1

Answer: (c) = 360 cm³ 

Let a = 9 cm, b = 12 cm, c = 15 cm. Then,

s = \(\frac{a+b+c}{2} = \frac{9+12+15}{2}\) = 18 cm

∴ Area of the base = \(\sqrt{s(s-a)(s-b)(s-c)}\) 

= \(\sqrt{18(18-9)(18-12)(18-15)}\)  

= \(\sqrt{18\times 9 \times 6\times 3}\)  = 54 cm²

∴ Volume of the tetrahedron 

= \(\frac{1}{3}\) × (Area of the base × height)

= \(\frac{1}{3}\) × 54 × 20 cm³ 

= 360 cm³