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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.
Solution
(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 `
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