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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
- height of the cone
- slant height of the cone
- curved surface area of the cone
`["Assume "pi=22/7]`
Solution
(i) Radius of cone = `(28/2) cm` = 14 cm
Let the height of the cone be h.
Volume of cone = 9856 cm3
⇒ `1/3pir^2h` = 9856 cm3
⇒ `[1/3xx22/7xx(14)^2xxh]cm^2` = 9856 cm3
h = 48 cm
Therefore, the height of the cone is 48 cm.
(ii) Slant height (l) of cone = `sqrt(r^2+h^2)`
= `[sqrt(14^2+48^2)]cm`
= `[sqrt(196+2304)]cm`
= 50 cm
Therefore, the slant height of the cone is 50 cm.
(iii) Curved surface area of cone = πrl
= `(22/7xx14xx50)cm^2`
= 2200 cm2
Therefore, the curved surface area of the cone is 2200 cm2.
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