Question

If the ratio of radius of base and height of a cone is 5 : 12 and its volume is 314 cubic metre. Find its perpendicular height and slant height (π = 3.14).

Answer 1

Given: Ratio of radius of base and height of a cone = 5 : 12, 

Volume = 314 cubic metre 

To find: Perpendicular height (h) and slant height (l) 

i. The ratio of radius and height of cone is 5 : 12 

Let the common multiple be x. 

∴ Radius of base (r) = 5x 

Perpendicular height (h) = 12x

∴ x³ = 1 

∴ x = 1 … [Taking cube root on both sides] 

∴ r = 5x = 5(1) = 5m 

h = 12x = 12(1) = 12 m 

ii. Now, l² = r² + h² 

= 5² + 12² 

= 25 + 144 

∴ l² = 169

∴ l = √169 … [Taking square root on both sides] 

= 13 m 

The perpendicular height and slant height of the cone are 12 m and 13 m respectively.