The radius and height of a right circular cone are in the ratio 5 : 12

1.	The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the slant height and radius of the cone. (Use π = 3.14)
Answer» We have, Let radius of cone r = 5x Let height h = 12x ∴ Volume = 2512 m³ = \(\frac{1}{3}\)×3.14×25x²×12x = 2512 = x³ = 8 = x = 2 ∴r = 10 and h = 24 cm Hence, slant height l = \(\sqrt{r^2+h^2}\) = l =\(\sqrt{100+576}\) = 26 m

The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the slant height and radius of the cone. (Use π = 3.14)

Answer»

We have,

Let radius of cone r = 5x

Let height h = 12x

∴ Volume = 2512 m³

= \(\frac{1}{3}\)×3.14×25x²×12x = 2512

= x³ = 8

= x = 2

∴r = 10 and h = 24 cm

Hence,

slant height l = \(\sqrt{r^2+h^2}\)

= l =\(\sqrt{100+576}\)

= 26 m