# NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.5 – Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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 =

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