Question

The area of the base of a right circular cone is 154 cm² and its height is 14 cm. Its curved surface area is ______.

Options

• 154`sqrt(5)  "cm"^2`

• `154 sqrt(7)  "cm"^2`

• `77sqrt(7)  "cm"^2`

• `77sqrt(5)  "cm"^2`

Answer 1

The area of the base of a right circular cone is 154 cm² and its height is 14 cm. Its curved surface area is `underlinebb(154 sqrt(5)  "cm"^2)`.

Explanation:

Area of the base of the of a right circular cone = πr²

Therefore,

`=> 22/7xx"r"^2 = 154`

`=> "r"^2 = (154xx7/22)`

⇒ r² = 49

⇒ r = 7 cm

Now, r = 7 cm and h = 14 cm

Then, slant height of the cone, `l = sqrt("r"^2 + "h"^2)` 

`=sqrt((7)^2 + (14)^2)`

`=sqrt(49 + 196)`

`= sqrt(245)`

`= 7sqrt(5)  "cm"`

Hence, the curved surface area of the cone = πrl

`= (22/7xx7xx7xxsqrt(5)) "cm"^2`

`=154 sqrt(5)  "cm"^2`