The curved surface area of a right circular cone is 5400π cm², and the diameter of its base is 144 cm. Find the height (in cm) of the cone.

Correct option is B

Given:

Curved surface area (CSA) = 540$$0\pi\ \text{cm}^2$$​​

Diameter = 144 cm

r = 72 cm

Formula Used:

CSA of cone:  $$\text{CSA}=\pi$$​r l 

Relation: $$l^2=r^2+h^2$$​

h$$=\sqrt{l^2-r^2}$$​​

Solution:
From CSA: $$\pi r l = 5400\pi \implies r l = 5400 \implies 72l=5400 \implies l=75\ \text{cm}$$​​
Then
h=$$\sqrt{l^2-r^2}=\sqrt{75^2-72^2}=\sqrt{(75-72)(75+72)}=\sqrt{3\times147}$$​​
​$$=\sqrt{441}=21\ \text{cm}$$​.
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