NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.6 – Part 1

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Formulas for volume of common solids

Volumes of Common Solids

Formulas for volume of common solids

Q-1 The circumference of the base of a cylindrical vessel is Equation and its height is Equation . How many liters of water can it hold? ( Equation )

Solution:

  • Let, the radius of the cylindrical vessel be Equation

  • Height (h) of vessel Equation

  • Circumference of vessel Equation

    We know that, circumference of the base of the cylindrical vessel

    • Equation

    • Equation

    • Equation

    • Equation

    Therefore, capacity of the cylindrical vessel

  • Equation

  • Equation

  • Equation

  • Equation (Since, Equation )

  • Equation

Therefore, vessel can hold Equation liters of water.

Q-2 The inner diameter of a cylindrical wooden pipe is Equation and its outer diameter is Equation . The length of pipe is Equation . Find the mass of the pipe, if Equation of wood has a mass of Equation .

Solution:

  • Inner diameter Equation

  • Therefore, inner radius (r) = Equation Equation

  • Outer diameter Equation

  • Therefore, outer radius(R) Equation Equation

  • Outer volume Equation

  • Inner volume Equation

Since the inner volume is empty, volume of the wood used = outer volume - inner volume

  • Equation

  • Equation

Since, Equation of wood has a mass of Equation , therefore mass of the pipe = Equation

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