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

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Calculation of volume for cube and cuboid

Calculation of Volume of Cube and Cuboid

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Q-8 A solid cube of side 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

Therefore, volume of the cube

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

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

Surface area of the cube

Therefore, ratio of their surface area = = or

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

Solution:

  • River depth

  • River width

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

Therefore in one minute length of river falls in the sea. That is, in one minute a cuboid of length , 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 =