Question

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

Answer 1

(1) Given that, 

Slant height of cone= 14cm  

Let radius of circular end of cone=r 

Curved surface area of cone=`pirh` 

`308cm^2=(22/7xxrxx14)cm`        [∵` CSA=308 cm^2`] 

⇒ `r= 308/44cm=7cm` 

Thus, radius of circular end of cone= 7cm 

(ii) Given that CSA= `308cm^2` 

WKT, total surface area of cone 

=curved surface area of cone + area of base 

= `pirl+pir^2` 

=`[308+22/7(7)^2]cm^2` 

= `308+154cm^2` 

= `462cm^2` 

Thus, the total SA of the cone is `462 cm^2`