Question

the dimension of a metal block on 120 cm into 90 cm into 75 cm. It is a melted can recast into cubes of Edge 30 cm. how many cubes will be formed​

Answer 1

Answer:

Number of Cubes formed are 30.

Step-by-step explanation:

Given :

Dimensions of the metal block = 120 cm × 90 cm × 75 cm

Side of the cube = 30 cm

To find :

Cubes made out of the melted metal box

Solution :

$\boxed{\sf{Number \: of \: Cubes = \dfrac{Volume\:of\:Cuboid}{Volume\:of\:Cube}}}$

★ $\textsf{\underline{\underline{Volume of Cuboid : }}}$

$\sf{Formula} = \purple{Length \times Breadth \times Height}$

$\sf{\implies} \: 120 \times 90 \times 75 \\ \\ \sf{\implies} \:10800 \times 75 \\ \\ \sf{\implies} \:810000 \: {cm}^{3}$

$\rule{300}{1.5}$

★ $\textsf{\underline{\underline{Volume of Cube : }}}$

$\sf{Formula=\purple{Side^{3}}}$

$\sf{\implies} \: {30}^{3} \\ \\ \sf{\implies} \:27000 \: {cm}^{3}$

$\rule{300}{1.5}$

★ $\textsf{\underline{\underline{Number of Cubes :}}}$

$\sf{\implies} \: \dfrac{Volume\:of\:Cuboid}{Volume\:of\:Cube} \\ \\ \sf{\implies} \: \dfrac{810000}{27000} \\ \\ \sf{\implies} \: \dfrac{810}{27} \\ \\ \sf{\implies} \:30$

Number of Cubes formed = 30

$\therefore$ Number of Cubes formed are 30.

Answer 2

Answer : 30 Cubes

$\rule{100}$

Step - By - Step Explanation :

It is stated that the dimensions of metal block are :-

• Length = 120 cm
• Breadth = 90 cm
• Height = 75 cm

It means that the metal block is in cuboidal shape.

Also,

It is melted into cubes of Edge = 30 cm.

We know that,

$\sf Number\:of\:cubes=\dfrac{Volume\:of\:metal\:block}{Volume\:of\:one\:cube}$

∵ Volume of Cuboid = length × breadth × height

∵ Volume of Cube = ( Edge )³

Now,

Put the given values in the formula. We get,

$\sf Number\:of\:cubes\:needed =\dfrac{120\times 90\times 75}{(30)^3}$

$\sf = \dfrac{120\times 90\times 70}{2700}$

$\sf =\dfrac{12\times 9\times 75}{270}$

$\sf =\dfrac{2\times 75}{5}$

$\sf = 2\times 15$

$\sf = 30$

Hence,

30 cubes will be formed.

$\rule{100}2$

Hey, Do you know ?

→ The Oxford and the Merriam-Webster dictionaries say the word " Mathematics " is plural because of the letter 's' in the end.

→  Google, derived its name from the word 'googol' -- a mathematical term for the number 1 followed by 100 zeros, which reflect infinite amount of search on the internet.

$\rule{200}2$

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