Question

In the packet of 8 cm X 8cm X 8cm X, how many match boxes will come of the total volume of 1cm X 1cm X 1cm? Is the number equal to the volume of the packet or not?
Answer​

Answer 1

Answer:

88 boxes can be stored in the packet.

Volume of packet = No. of matchboxes that can be stored in it

Solution:

⇒ Given

Length of the packet = 8 cm

Breadth of the packet = 8 cm

Height of the packet = 8 cm

Length of the matchbox = 1 cm

Breadth of the matchbox = 1 cm

Height of the matchbox = 1 cm

First of all, we need to find the volume of the big packet by applying the formula of volume of a cube.

Formula:

$\sf{\boxed{Volume\:of\:cube=a^3}}$

We know that a is 8 cm.

Hence volume of cube

= 8³

= 8 x 8 x 8

= 512 cm³

Now we need to find the volume of each small matchbox. It can also be found by applying the formula of volume of a cube.

Formula:

$\sf{\boxed{Volume\:of\:cube=a^3}}$

We know that a is 1 cm.

Hence volume of cube

= 1³

= 1 x 1 x 1

= 1 cm³

Last, we need to find the no. of matchboxes. We can find this by dividing the volume of one matchbox from the total volume of the packet.

Formula:

$\sf{\boxed{No.\:of\:matchboxes=\dfrac{Volume\:of\:packet}{Volume\:of\:one\:packet}}}$

Substituting the values in the equation:

$\sf{No.\:of\:matchboxes=\dfrac{88}{1}}$

$\sf{88\:boxes}$

Hence the required answer is 88 boxes.

It is also stated in the question whether the no. of boxes is equal to the total volume of the packet.

Yes it is.

This is because each small box has the volume 1 cm³. Hence the packet can accommodate 88 small matchboxes.