Examveda
Examveda

The volume of a right circular cone is 1232 cm3 and its vertical height is 24 cm. Its curved surface area is

A. 154 cm2

B. 550 cm2

C. 604 cm2

D. 704 cm2

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & {\text{Volume of a cone}} = \frac{1}{3}\pi {r^2}h \cr & \frac{1}{3}\pi {r^2}\left( {24} \right) = 1232{\text{ c}}{{\text{m}}^2} \cr & {r^2} = \frac{{1232 \times 3 \times 7}}{{24 \times 22}} \cr & {r^2} = 7 \times 7 \cr & r = \sqrt {7 \times 7} \cr & r = 7{\text{ cm}} \cr & l = \sqrt {{r^2} + {h^2}} \cr & = \sqrt {{7^2} + {{24}^2}} \cr & = \sqrt {625} \cr & = 25 \cr & {\text{Curved surface area}} = \pi rl \cr & = \frac{{22}}{7} \times 7 \times 25 \cr & = 550{\text{ c}}{{\text{m}}^2} \cr} $$

This Question Belongs to Arithmetic Ability >> Mensuration 3D

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