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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 - Mathematics

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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

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

 

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Solution

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

Let the height of the cone be h.

Volume of cone = 9856 cm3

`rArr1/3pir^2h = 9856 cm^3`

`rArr[1/3xx22/7xx(14)^2xxh]cm^2=9856cm^3`

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) CSA of cone = πrl

`=(22/7xx14xx50)cm^2`

= 2200 cm2

Therefore, the curved surface area of the cone is 2200 cm2.

Concept: Volume of a Right Circular Cone
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APPEARS IN

NCERT Class 9 Maths
Chapter 13 Surface Area and Volumes
Exercise 13.7 | Q 6 | Page 233

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