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 ways. Find the difference in volumes of the two cones so formed. Also, find their curved surfaces.

Answer 1

Height of the cone (h₁) = 3 cm 

Radius of the cone (r₁) = 4 cm 

Slant height of the cone (l₁) = 5 cm 

Volume of cone (V₁) = \(\frac{1}3πr^2h\)

= \(\frac{1}3π\times4^2\times3\) cm³

= 16π cm³

Again after rotating 

Height of the cone (h₂) = 4 cm 

Radius of the cone (r₂) = 3 cm 

Slant height of the cone (l₂) = 5 cm 

Volume of cone (V₂) = \(\frac{1}3πr^2h\) 

= \(\frac{1}3π\times3^2\times4\)cm³ 

= 12π cm³ 

Difference between the volume two cones =16π – 12π = 4π

= 4π  cm³ 

Curved surface area of first cone =π × r₁× l₁ 

= π × 4 × 5 

= 20π cm² 

Curved surface area of second cone = π x r₂ x l₂

= π x 3 x 5

= 15π cm²