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

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

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