NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.5 – Part 3

Calculation of volume for cube and cuboid

Calculation of Volume of Cube and Cuboid

Calculation of volume for cube and cuboid

Q-8 A solid cube of side Equation is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

Solution:

Edge of the cube Equation

Therefore, volume of the cube Equation

  • Equation

  • Equation

The big cube is cut into 8 equal smaller cubes, therefore volume of each of the smaller cube Equation

Let, side of the smaller cube Equation , then, we have Equation or Equation

Surface area of the cube Equation

Therefore, ratio of their surface area = Equation = Equation or Equation

Q-9 A river Equation deep and Equation wide is flowing at the rate of Equation per hour. How much water will fall into the sea in a minute?

Solution:

  • River depth Equation

  • River width Equation

Rate of flow of water is Equation per hour. We need to convert this to m per minute according to the units used in our question. Equation ( Equation ) = Equation per minute.

Therefore in one minute Equation length of river falls in the sea. That is, in one minute a cuboid of length Equation , width 40 m (the breadth of river) and height 3 m (depth of river) falls in the sea.

Volume of water flowing into the sea in a minute = Equation

  • Equation

  • Equation

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