Question

show me many examples of volume of cube with question and answer​

Answer 1

Cube:

A cube is a three-dimensional figure with 6 square faces. It has 6 faces, 8 vertices and 12 edges. The basic formulae related to a cube are:

➡ Lateral Surface Area = 4a²

➡ Total Surface Area = 6a²

➡ Volume = a³

Here we will be emphasizing on the volume formula which is a³.

Examples:

Example 1:

A toy cube has a side of length 5 cm. Find its volume.

Side, a = 5 cm

Volume = a³

Volume = 5³

= 5 x 5 x 5

= 125 cm³

The volume of the toy cube is 125 cm³.

Example 2:

Soil is dug out of a cubical pit of height 10 m. Find the volume of soil dug out.

Side/Height, a = 9 m

Volume = a³

Volume = 9³

= 9 x 9 x 9

= 720 m³

The volume of soil dug out of 720 m³.

Example 3:

Find the amount of water, a cubical swimming pool of dimensions 10 m x 10 m x 10 m.

Dimensions of the swimming pool = 10 m x 10 m x 10 m

Volume = a³

Volume = 10³

= 10 x 10 x 10

= 1000 m³

The amount of water that the cubical swimming pool can hold is 1000 m³.

Example 4:

A huge cubical box of side 6 cm is made up of cubes of side 1 cm. Find the number of smaller cubes the larger cube can hold.

Side of smaller cube = 1 cm

Volume = a³

Volume = 1³ = 1 cm³

Side of larger cube = 6 cm

Volume = a³

Volume = 6³ = 216 cm³

No. of smaller cubes the large cube can hold:

$\sf{\longrightarrow\:\dfrac{Volume\:of\:larger\:cube}{Volume\:of\:smaller\:cube}}$

$\sf{\longrightarrow\:\dfrac{216}{1}}$

= 216 cubes

The huge cube can hold 216 smaller cubes.

Example 5:

Find the volume of a large cubical box of dimensions 80 cm x 80 cm x 80 cm.

Side, a = 80 cm

Volume = a³

Volume = 80³

= 80 x 80 x 80

= 512000 cm³

The volume of the cardboard box is 512000 cm³.

Volume:

The volume of any three dimensional figure refers to the amount of material used to make the figure/the amount of material that can be stored inside the figure.

Volume is represented as cm³ or m³.