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
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.
☛ Related Questions:
- The height of a cone is 15 cm. If its volume is 1570 cm3, find the radius of the base. (Use π = 3.14)
- If the volume of a right circular cone of height 9 cm is 48π cm3, find the diameter of its base.
- A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?
- 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
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