Page 226 - Math_Genius_V1.0_C5_Flipbook

E:\Working\Focus_Learning\Math_Genius_5_(05-10-2023)\Open_Files\CHAP_11
\\November 22, 2023 5:10 PM Surender Prajapati Proof 5 Reader _________________________ Date: ___________________74

VolUme

We know that plane figures have only two dimensions—length and breadth.

But solid figures or shapes have three dimensions—length, breadth (or width) and thickness

(height).
So, solids shapes are called three-dimensional (3-d) shapes.

Cuboid Cube Cone Cylinder Sphere

And the amount of space occupied by a solid is called its volume. Here are two boxes.
Can you say which is bigger? To compare both boxes, we need
unit cubes.

It is a unit cube. That means length, breadth and height of
it is 1 unit each. Now, we fill both the boxes with the unit cubes

layers by layer. Put the layers of unit cubes in both the boxes till Box-A Box-B
they are completely filled.

Box-A (Layer-1) Box-B Box-A (Layer-2) Box-B Box-A Box-B
We observe that Box-A contains 5 layers of unit cubes and each layer contains 18 cubes,

i.e., 5 × 18 = 90 unit cubes and Box-B contains 7 layers of unit cubes and each layer
contains 12 cubes, i.e., 7 × 12 = 84 unit cubes.

Thus, Box-A has more number of unit cubes than the Box-B.
Since the dimension of unit cube is 1 unit, the volume of unit cube is 1 cubic unit.

Hence, the volume of Box-A is 90 cubic units and the volume of Box-B is 84 cubic units.

So, Box-A has a larger volume than Box-B.
Remember
The volume of a unit cube is 1 cubic unit.
In cubic units, cubic
1 unit stands for the three
measurements of length,
1 unit
1 unit breadth and height.

The unit of volume of a cube with a side in cm is cubic cm. 1 unit

The unit of volume of a cube with a side in m is cubic m. 1 unit
1 unit

224 Mathematics-5