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» Let the ratio of radius and height of a right circular cone be y. Radius of cone(r) = 5 y Height of cone (h) =12 y Now we know, l² = r² + h² = (5y)² + (12y)² = 25 y² + 144 y² or l = 13y Now, volume of the cone is given 2512 cm³ ⇒\(\frac{1}{3}\)πr²h = 2512 ⇒ \(\frac{1}{3}\) x 3.14 x (5y)² x 12y = 2512 ⇒ y³ = (2512 x 3)/(3.14 x 25 x 12) = 8 or y = 2 Therefore, Radius of cone = 5y = 5 x 2 = 10 cm Slant height (l) = 13y = 13 x 2 = 26 cm

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»

Let the ratio of radius and height of a right circular cone be y.

Radius of cone(r) = 5 y

Height of cone (h) =12 y

Now we know,

l² = r² + h²

= (5y)² + (12y)²

= 25 y² + 144 y²

or l = 13y

Now, volume of the cone is given 2512 cm³

⇒\(\frac{1}{3}\)πr²h = 2512

⇒ \(\frac{1}{3}\) x 3.14 x (5y)² x 12y = 2512

⇒ y³ = (2512 x 3)/(3.14 x 25 x 12)

= 8

or y = 2

Therefore,

Radius of cone = 5y = 5 x 2 = 10 cm

Slant height (l) = 13y = 13 x 2 = 26 cm