Question

The volume of a right circular cone is 9856 cm3. If the diameter of the base is 28 cm, find:
(i) height of the cone (ii) slant height of the cone (iii) curved surface area of the cone. 

Answer 1

(i) Radius of cone `= (28/2)cm=14 cm` 

Let height of cone is h 

Volume of cone`= 9856 cm^3` 

⇒` 1/3pir^2h=9856 cm^2` 

⇒` [1/3xx3.14xx7xx7xxh ] cm^2=9856cm^2` 

h=48 cm 

Thus the height of the cone is 48 . cm 

(2) Slant height (l) of cone =` sqrt(r^2+h^2)` 

=`(sqrt((14)^2+(48)^2cm)` 

=` sqrt(196+2304)=sqrt2500cm` 

= 50cm 

Thus, the slant height of cone is 50cm. 

(3) CSA of cone=`pirl=(22/7xx14xx50)cm^2` 

`=2200cm^2 `