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 12cm 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.


Edge of the cube =12cm.

Therefore, volume of the cube (side)3cm3

  • =(12×12×12)cm3

  • =1728cm3

The big cube is cut into 8 equal smaller cubes, therefore volume of each of the smaller cube 17288cm3=216cm3

Let, side of the smaller cube =a , then, we have a3=216 or a=6cm

Surface area of the cube =6(side)2

Therefore, ratio of their surface area = 6×12×126×6×6 = 41 or 4:1

Q-9 A river 3m deep and 40m wide is flowing at the rate of 2km per hour. How much water will fall into the sea in a minute?


  • River depth (h)=3m

  • River width (b)=40m

Rate of flow of water is 2km per hour. We need to convert this to m per minute according to the units used in our question. 2km=(200060)m/min ( 1km=1000m&1hr=60min ) = 1003m per minute.

Therefore in one minute 1003m length of river falls in the sea. That is, in one minute a cuboid of length 1003m , 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 = lbhm3

  • =(1003×40×3)m3

  • =4000m3

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