The curved surface area of a right circular cone is 6500π cm², and the diameter of its base is 100 cm. Find the height (in cm) of the cone.​

Correct option is B

Given:

Curved surface area (CSA) = $$6500\pi\ \text{cm}^2$$​​

Diameter = 100 cm

r = 50 cm

Formula Used:

CSA of cone=$$\pi r l$$​​

Slant height: $$l^2 = r^2 + h^2 \implies h=\sqrt{l^2-r^2}$$​​

Solution:
​$$\pi r l = 6500\pi \implies r l = 6500 \implies 50l=6500 \implies l=130\ \text{cm}$$

​From CSA,
Then  $$h=\sqrt{130^2 - 50^2} = \sqrt{16900 - 2500}=\sqrt{14400}=120\ \text{cm}$$​​