Question

8 cubes each of size 3cm have been kept to form another cube. Find the volume of new cube.

Answer 1

A cube is a solid box whose every surface is a square of same area.

Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure it is clear that 8 such cubes will fit in it. So the volume of the box will be equal to the volume of 8 unit cubes together.

Therefore, the volume of the cube = 8 cu cm

Note that 8 = 2 × 2 × 2

Thus, volume of a cube = side × side × side = side3

Hence, a cube has:

(i) six surfaces or faces,

(ii) 8 vertices,

(iii) 12 edges or sides of equal length.



Since a cube has all sides equal.

Volume of a cube = (side × side × side) cubic units.

= 1 × 1 × 1 cubic units

Since area = side × side

Volume of a cube = (area × side) cubic units.



 

Solved examples on volume of a cube:

1. Find the volume of a cube whose edge is 5 cm long.

The length of an edge = 5 cm

Volume of a cube = side of edge × side of edge × side of edge

Volume of a cube = 5 cm × 5 cm × 5 cm

                          = 125 cu cm

                          = 125 cm3


2. Find the volume of a cube of side 7 cm.

We know, volume of a cube = (side × side × side) cubic units.

Here, side = 7 cm.

               = 7 × 7 × 7 

               = 343

Therefore, volume of a cube = 343 cubic cm.


3. Find the volume of a cube of side 13 cm.

We know, volume of a cube =(side × side × side) cubic units.

Here, side = 13 cm.

                = 13 × 13 × 13

                = 2197

Therefore, volume of a cube = 2197 cubic cm.


4. Find the volume of water that can be contained in a cubical container each of whose edge measure 2 m internally.

The internal length of an edge of the container = 2 m

The internal volume of the container = 2 m × 2 m × 2 m = 8 cu m

The volume of water that the container can hold = the internal volume of the container.

Therefore, the required volume of water = 8 cu m.



 

● Volume.

Units of Volume

Cube.

Cuboid.

Practice Test on Volume.

Worksheet on Volume.







5th Grade Geometry 

5th Grade Math Problems 

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Answer 2

Answer:

216cm3

Step-by-step explanation:

side-3cm

volume-27cm3

no.of cubes-8

total-27*8=216cm3