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:

1. The volume and curved surface area of a cone are same.
2. 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

Given :-

Volume and CSA of cone is same

Product of radius and height = 36

To find :-

Slant height

Solution :-

Let

$\mid \pmb {Radius = r}\mid$

$\mid \pmb{Height = h}\mid$

$\mid \pmb{Slant \; height = l}\mid$

$\sf Volume \; of \; cone = CSA\; of \; cone$

$\sf \dfrac{1}{3} \pi r^2h = \pi rl$

$\sf \pi r^2 h = \pi rl \times 3$

$\sf r h = 3l$

$\sf 36 = 3l$

$\sf l = \dfrac{36}{3}$

l = 12 cm