Volume of a cube — lesson. Mathematics State Board, Class 9.

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Cube:

Cube is a special type of cuboid whose length, breadth and height are all equal.

Volume of a cube:

Let

$a$ be the edge length of the cube.

Volume of a cuboid

$=$

$lbh$ cu. units.

For a cube, length

$=$ breadth

$=$ height

$=$ edge

That is,

$l$

$=$

$b$

$=$

$h$

$=$

$a$

Substitute this in the volume of a cuboid formula.

Volume of a cuboid

$=$

$a \times a \times a$

$=$

$a^3$

$=$ Volume of a cube

Therefore, the volume of a cube

$=$

$a^3$ cu. units.

Example:

The edge of the cubical tank is

$5$

$m$ . Find how much water it holds in litres?

$[$ Hint:

$1 \ m^3 = 1000 \ l]$

Solution:

Edge of the cubical tank

$=$

$5$

$m$

Volume of the cubical tank

$=$

$a^3$

$=$

$5^3$

$=$

$5 \times 5 \times 5$

$=$

$125$

$m^3$

Now, convert

$m^3$ to

$l$ .

$1 \ m^3 = 1000 \ l$

$125 \ m^3 = 125 \times 1000 = 125000$

Therefore, the volume of the cubical tank is

$125000 \ l$ .

Important!

For any two cubes:

$\text{Ratio of surface areas}$

$=$

$(\text{Ratio of sides})^2$

$\text{Ratio of volumes}$

$=$

$(\text{Ratio of sides})^3$

$(\text{Ratio of surface areas})^3$

$=$

$(\text{Ratio of volumes})^2$

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2. Volume of a cube

Theory: