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

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

Solution:

  • Let, the radius of the cylindrical vessel be

  • Height (h) of vessel

  • Circumference of vessel

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

Therefore, capacity of the cylindrical vessel

  • (Since, )

Therefore, vessel can hold liters of water.

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

Solution:

  • Inner diameter

  • Therefore, inner radius (r) =

  • Outer diameter

  • Therefore, outer radius(R)

  • Outer volume

  • Inner volume

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

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