Find the capacity in litres of a conical vessel with
(i) radius 7 cm, slant height 25 cm
(ii) height 12 cm, slant height 13 cm

Solution:

Capacity of a conical vessel is nothing but the volume of the cone.

Volume of a cone of base radius r, and height h = 1/3πr²h

Slant height of the cone, l = √r² + h²

i) Radius of the conical vessel, r = 7cm

Slant height of the conical vessel, l = 25cm

Height of the conical vessel, h = √l² - r²

= √(25)² - (7)²

= √625 - 49

= √576

h = 24 cm

Capacity of the conical vessel = 1/3 πr²h

= 1/3 × 22/7 × 7 cm × 7 cm × 24 cm

= 1232 cm³

= 1232 × (1/1000L)   [∵ 1000 cm³ = 1litre]

= 1.232 litres

ii) Height of the conical vessel, h = 7cm

Slant height of the conical vessel, l = 13cm

Radius of the conical vessel, r = √l² - h²

= √(13)² - (12)²

= √169 -144

= √25

r = 5 cm

Capacity of the conical vessel = 1/3πr²h

= 1/3 × 22/7 × 5 cm × 5 cm × 12 cm

= 2200/7 cm³

= 2200/7 × 1/1000 l [∵ 1000 cm³ = 1litre]

= 11/35 litres

☛ Check: NCERT Solutions for Class 9 Maths Chapter 13

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Video Solution:

Find the capacity in litres of a conical vessel with (i) radius 7 cm, slant height 25 cm (ii) height 12 cm, slant height 13 cm

NCERT Solutions for Class 9 Maths Chapter 13 Exercise 13.7 Question 2

Summary:

We have found that the capacity of the first conical vessel with radius 7 cm, slant height 25 cm is 1.232 litres and the capacity of the second conical vessel with height 12 cm, slant height 13 cm is 11/35 litres.

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