The curved surface area of a right circular cone is 5904π cm², and the diameter of its base is 72 cm. Find the height (in cm) of the cone.​

Correct option is B

Given:

Curved Surface Area (CSA) of cone = 5904π cm²

Diameter of base = 72 cm

Radius r = $$\frac{72}{2}$$​ = 36 cm

Required: Height h of the cone.

Formula Used:

Curved Surface Area of a cone= π r l

where l = slant height

​$$l^2 = r^2 + h^2$$​​

Solution:

From CSA: 

5904π = π $$\times$$​36$$\times$$​ l 

 l = $$\frac{5904}{36}$$​ = 164 cm

Now, 

​$$(164)^2 = (36)^2 + h^2$$​​

h = $$\sqrt{164^2 - 36^2}$$​​

= $$\sqrt{(164+ 36)(164 - 36)}$$​​

= $$\sqrt{25600}$$​ = 160 cm