Question

a cuboid is made of metal it is 20 cm × 18 cm × 12 cm It is melted and recast into small cubes with an edge 3 cm in length how many cubes are made
​

Answer 1

Given -

• Dimensions of cuboid = 20cm × 18cm × 12cm

• Edge of each cube = 3cm

To find -

• Number of cubes, made by recasting of cuboid.

Formula used -

• Volume of cube and cuboid.

Solution -

In the question we are, given with the length, breadth and height of a cuboid, and when it was melted and recasts into small cubes, their edge is 3cm, and we need to find the number cubes, that has been made. For that, first we will find the volume of cuboid and then volume of cube, after that, we will divide the volume of cuboid by the volume of cube, that will give us the number of cubes. Let's do it!

According to question -

$\sf Length_{(of cuboid)}$ = 20cm

$\sf Breadth_{(of cuboid)}$ = 18cm

$\sf Height_{(of cuboid)}$ = 12cm

Also -

$\sf Edge_{(of\:each\:cube)}$ = 3cm

Now -

First let's find the volume of cuboid, by using the formula of volume of cuboid, for that we need, length, breadth and height of cuboid, then we multiply them, and from that we get our volume.

$\sf \underline{\: volume \: of \: cuboid = l \: \times \: b \: \times \: h}$

On substituting the values -

$\sf \longrightarrow \: v \: = 20cm \: \times \: 18cm \: \times \: 12cm$

$\sf \longrightarrow \: v \: = 4320 \: {cm}^{3}$

Similarly -

We will find the volume of cube, by multiplying the edge, 3 times with itself.

$\sf \underline{volume \: of \: cube} \: = {(a)}^{3}$

On substituting the values -

$\sf \longrightarrow \: v \: {(3)}^{3}$

$\sf \longrightarrow \: v \: = 27 \: {cm}^{3}$

At the end -

We will divide the volume of cuboid, with the volume of cube, that will give us the number of cubes.

$\sf \underline{no. \: of \: cubes} \: = \dfrac{volume \: of \: cuboid}{volume \: of \: cube}$

On substituting the values -

$\sf \longrightarrow \: number_{(of\:cubes)} = \cancel \dfrac{4320}{27}$

$\sf \longrightarrow \: number_{(of\:cubes)} \: = 160 \: cubes$

$\therefore$ 160 cubes can be made from that cuboid.

______________________________________________________

Answer 2

Given :-

• Length of cuboid = 20 cm
• Breadth of cuboid = 18 cm
• Height of cuboid = 12 cm
• Edge of cube = 3 cm

To Find :-

How many cubes can made

Summary of formula :-

$\sf \: Volume(cuboid) \: = l \times b \times h$

Here,

L is the length

B is the Breadth

H is the Height

$\sf \: Volume(cube) = {edge}^{3}$

Procedure :-

At first we will find the Volume of cuboid and then we will find volume of cube and after we will divide the Volume of Cuboid/Volume of cube

Calculation :-

$\sf \implies \: Volume = 20 \times 18 \times 12$

$\sf \implies \: Volume = 360 \times 12$

$\sf \implies \: Volume \: = 4320 \: cu \: cm$

Now,

Finding volume of cube

$\sf \implies \: Volume \: = {3}^{3}$

$\sf \implies \: Volume = 9 \times 3$

$\sf \implies \: Volume = 27 {cm}^{3}$

Total cubes = 4320/27

$\frak \pink{Total \: cubes \: = 160}$