How many meters of cloth 5.2 metre wide will be required to make a conical tent, the radius of whose base is 10 m and height is 24 m?

A 60π m

B 50π m

C 55π m

D 57π m

E None of these

Correct Answer: Option B

Given,

Radius of the base of the cone (R) = 10 m

Height of the Cone (H) = 24 m

∵ Slant height (l) = \(\sqrt {\left( {{R^2}{\rm{\;}} + {\rm{\;}}{H^2}} \right)}\)

∴ Slant Height = \(\sqrt {{{10}^2} + {{24}^2}} = 26{\rm{\;}}m\)

We know,

Curved Surface Area of the cone = πRl

∴ Curved Surface Area = π x 10 x 26 = 260π m²

Area of the cloth used = Curved Surface Area of the cone = 260π m²

Given, width of the cloth = 5.2 m

Length of the cloth used = Area of Cloth used/Width of Cloth

∴ Length of the cloth = 260π/5.2 = 50π