The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000 cm³ = 1 l)

Solution:

Since the base of a cylindrical vessel is a circle, so its radius can be easily obtained using the circumference = 2πr

The volume of a cylinder of base radius, r and height, h = πr²h

Let the radius of the base be 'r'

Height of the cylinder, 'h' = 25 cm

Circumference of the base = 132 cm

2πr = 132 cm

r = 132 / 2π

= (132 / 2) × (7 / 22)

= 21 cm

The capacity of the cylindrical vessel = πr²h

= 22/7 × 21 cm × 21 cm × 25 cm

= 34650 cm³

= 34650/1000 (Since 1000 cm³ = 1 L)

= 34.65 L

☛ Check: NCERT Solutions Class 9 Maths Chapter 13

Video Solution:

The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000 cm³ =1 l)

Class 9 Maths NCERT Solutions Chapter 13 Exercise 13.6 Question 1

Summary:

It is given that the circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. We have found that the capacity of the cylindrical vessel is 34.65 litres.

☛ Related Questions:

• The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 g.
• A soft drink is available in two packs - (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm, and (ii) a plastic cylinder with a circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?
• If the lateral surface of a cylinder is 92.4 cm3 and its height is 5 cm, then find(i) radius of its base(ii) its volume. (Use π = 3.14)
• It costs ₹2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of ₹20 per m2, find.(i) inner curved surface area of the vessel,(ii) radius of the base,(iii) capacity of the vessel.