The curved surface area of a right circular cone is 2684π cm², and the diameter of its base is 44 cm. Find the height (in cm) of the cone.​

Correct option is D

Given:

Curved surface area (C.S.A) of the cone = 2684π cm²

Diameter of the cone's base = 44 cm

We need to find the height (h) of the cone.

Formula Used:

Curved surface area (C.S.A) of a cone = πrl

Slant height, l = $$\sqrt{r^2 + h^2}$$​​

Solution:

The diameter of the base is 44 cm, so the radius r = $$\frac{44}{2}$$​ = 22 cm

Now, 

2684π = π × 22 × l

2684 = 22 × l

l = $$\frac{2684}{22}$$​ = 122 cm

So, slant height formula;

$$122^2 = 22^2 + h^2$$​​

14884 = 484 + $$h^2$$​​

$$h^2$$​ = 14884 - 484 = 14400

h = $$\sqrt{14400}$$​ = 120 cm

The height of the cone is 120 cm