NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.6 – Part 2

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Cylinder volume=πr^2 h

Cylinder Volume

Cylinder volume=πr^2 h

Q-3 A soft drink is available in two packs

  1. A tin can with a rectangular base of length and width , having a height of and

  2. A plastic cylinder with circular base of diameter and height

Which container has greater capacity and by how much?

Solution (i)

Capacity of tin can

Capacity

Solution (ii)

Capacity or volume of plastic cylinder is given as

Diameter , therefore radius(r)

Height (h)

Therefore, capacity

Clearly the second container, the plastic cylinder has greater capacity than the first container, a tin can. The cylinder has more volume.

Q-4 If the lateral surface of a cylinder is and its height is ,and then find

  1. Radius of its base

  2. Its volume .( )

Solution:

  1. Consider the radius of the cylinder be

    Height

    • Later surface area

    So, the radius of the base is

  2. Now, volume of cylinder

Q-5 It costs to paint the inner curved surface of a cylindrical vessel deep. If the cost of painting is at the rate of find

  1. Inner curved surface area of the vessel

  2. Radius of the base

  3. Capacity of the vessel

Solution:

  1. Inner curved surface area of the vessel

  2. Radius of the base

    • Consider the radius of the base

    • The height of the cylindrical vessel

    We know that inner curved surface area

    • Therefore,

    So, the radius of the base is

  3. Capacity of the vessel