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

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 Equation and width Equation , having a height of Equation and

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

Which container has greater capacity and by how much?

Solution (i)

Capacity of tin can

  • Equation

  • Equation

  • Equation

Capacity Equation

  • Equation

  • Equation

Solution (ii)

Capacity or volume of plastic cylinder is given as Equation

Diameter Equation , therefore radius(r) Equation

Height (h) Equation

Therefore, capacity Equation

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

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

  1. Radius of its base

  2. Its volume .( Equation )

Solution:

  1. Consider the radius of the cylinder be Equation

    Height Equation

    • Later surface area Equation

    • Equation

    • Equation

    • Equation

    • Equation

    So, the radius of the base is Equation

  2. Now, volume of cylinder Equation

  • Equation

  • Equation

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

    • Equation

    • Equation

    • Equation

  2. Radius of the base

    • Consider the radius of the base Equation

    • The height of the cylindrical vessel Equation

    We know that inner curved surface area Equation

    • Therefore, Equation

    • Equation

    • Equation

    • Equation

    • Equation

    So, the radius of the base is Equation

  3. Capacity of the vessel Equation

  • Equation

  • Equation

  • Equation

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