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Find the capacity in litres of a conical vessel with radius 7 cm, slant height 25 cm - CBSE Class 9 - Mathematics

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Question

Find the capacity in litres of a conical vessel with radius 7 cm, slant height 25 cm

`["Assume "pi=22/7]` 

 

Solution 1

Radius (r) of cone = 7 cm

Slant height (l) of cone = 25 cm

`"Height (h) of cone "=sqrt(l^2-r^2)`

`=(sqrt(25^2-7^2))cm`

= 24 cm

`"Volume of cone "=1/3pir^2h`

`=(1/3xx22/7xx(7)^2xx24)cm^3`

= (154 x 8)cm3

= 1232 cm3

Therefore, capacity of the conical vessel

`= (1232/1000)litres"           "("1 litre "=1000cm^3)`

= 1.232 litres

Solution 2

The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as

Volume = `1/3 pi r^2 h`

 In a cone, the base radius ‘r’ is given as 7 cm and the slant height ‘l’ is given as 25 cm.

To find the base vertical height ‘h’ we use the relation between rl and h.

We know that in a cone

`l^2 = r^2 + h^2`

`h^2 = l^2 - r^2`

`h = sqrt(l^2 - r^2)`

`= sqrt(25^2 - 7^2)`

`= sqrt(625-49)`

` = sqrt(576)`

= 24

Therefore the vertical height is, h = 24 cm.

Substituting the values of r = 7 cm and h = 24 cm in the above equation and using ` pi = 22/7`

Volume = `((22)(7)(7)(24))/((3)(7))`

= (22) (7) (8) 

= 1232

Hence the volume of the given cone with the specified dimensions is `1232  cm^3`

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Class 9 (2018 to Current)
Chapter 13: Surface Area and Volumes
Ex.13.70 | Q: 2.1 | Page no. 233
 RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 20: Surface Areas and Volume of A Right Circular Cone
Ex.20.20 | Q: 2.1 | Page no. 20
Solution Find the capacity in litres of a conical vessel with radius 7 cm, slant height 25 cm Concept: Volume of a Right Circular Cone.
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