Question

Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find

1. radius of the base and
2. total surface area of the cone.

`["Assume "pi =22/7]`

Answer 1

(i) Slant height (l) of cone = 14 cm

Let the radius of the circular end of the cone be r.

We know, Curved surface area of cone = πrl

`(308)cm^2` = `(22/7xxr xx14)cm`

⇒ r = `(308/44)cm` = 7cm

Therefore, the radius of the circular end of the cone is 7 cm.

(ii) Total surface area of cone = Curved surface area of cone + Area of base

= πrl + πr²

= `[308+22/7xx(7)^2]cm^2`

= (308 + 154) cm²

= 462 cm²

Therefore, the total surface area of the cone is 462 cm².