Question

The volume and curved surface area of a cone are same. If the product of radius and height of the cone is

36 cm, then the slant height of the cone is:​

Answer 1

Answer:

The slant height of the cone is 12 cm.

Step-by-step explanation:

Given that:

The volume and curved surface area of a cone are same.

The product of radius and height of the cone is 36 cm.

To Find:

The slant height of the cone.

Finding the slant height of the cone:

Volume of a cone = Curved surface area of a cone

⟶ (πr²h)/3 = πrl

⟶ πr²h = 3πrl

Cancelling π and r both sides.

⟶ rh = 3l

⟶ 36 = 3l [Given]

⟶ l = 36/3

⟶ l = 12

∴ The slant height of the cone = 12 cm

Answer 2

Answer:

From given data

$\frac{\pi {r}^{2}h}{3} = \pi \: rl$

$rh = 3l$

$36 = 3l \: \: \: \: (given)$

$l = 12$