Question

A right angled triangle whose sides are 3 cm, 4 cm and 5 cm is revolved about the sides containing the right angle in two days. Find the difference in columes of the two cones so formed. Also, find their curved surfaces.

Answer 1

(i) Given that radius of cone(r₁) = 4cm

Height of cone (h₁) 3cm

Slant height of cone(l₁) = 5cm

Volume of cone`(V_1)=1/3pir_1^2h_1`

`=1/3pi(4)^2(3)=16picm^3`

(ii) Given radius of second cone (r₂) = 3cm

Height of cone(h₂) = 4cm

Slant height of cone (l₂) = 5cm

Volume of cone`(V_2)=1/3r_2^2h_2`

`=1/3pi(3)^2(4)=12picm^3`

Difference in volumes of two cones(V) = V₁ - V₂

V = 16π - 12π

V = 4πcm³

Curved surface area of first cone(S₁) = πr₁l₁

S₁ =π( 4)(5) = 20πcm²

Curved surface area of second cone(S₂) = πr₂l₂

S2 = π(3)(5) = 15πcm²

S₁ = 20πcm² S₂ = 15πcm²