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

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Answer in Brief

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

`["Assume "pi=22/7]` 

 

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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`

Concept: Volume of a Right Circular Cone
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 20 Surface Areas and Volume of A Right Circular Cone
Exercise 20.2 | Q 2.1 | Page 20
NCERT Class 9 Maths
Chapter 13 Surface Area and Volumes
Exercise 13.7 | Q 2.1 | Page 233

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