NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.5 – Part 1

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Formulas for volume of common solids

Volumes of Common Solids

Formulas for volume of common solids

Q-1 A matchbox measures Equation . What will be the volume of a packet containing Equation such boxes?

Solution:

  • Each matchbox measures Equation

  • Therefore, Equation , Equation and Equation

Volume of one matchbox

  • Equation

  • Equation

  • Equation

Volume of a packet containing Equation such boxes

  • Equation

  • Equation

Q-2 A cuboidal water tank is Equation long, Equation wide and Equation deep. How many litres of water can it hold? ( Equation )

Solution:

  • Dimensions of water tank Equation

  • Equation

Therefore Volume of the tank

  • Equation

  • Equation

  • Equation

Therefore, the tank can hold

  • Equation [Note that, 1 Equation ]

  • Equation Liters of water.

Q-3 A cuboidal vessel is Equation long and Equation wide. How high must it be made to hold Equation cubic metres of a liquid?Solution:

We know that,

  • Length Equation ,

  • Breadth Equation

  • Volume Equation

Volume of cuboid Equation

Therefore, Height Equation = Equation

Q-4 Find the cost of digging a cuboidal pit Equation long, Equation broad and Equation deep at the rate of Equation

Solution:

We know,

  • Equation

  • Equation

  • Equation

Volume of the pit

  • Equation

  • Equation

  • Equation

Rate of digging is Equation . Therefore, total cost of digging the pit = Equation

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