Question

a rectangular metallic block is 50cm*20cm*8cm. if it is melted and reformed into cubical block find the lenght of the edge of the cube. please answer me its important

Answer 1

Answer :-

$\: \: \underline{\boxed{\sf{\blue{Let's \: look \: at \: the \: analysis \: of \: the \: question \: first}}}}$

Here the concept of Volume of Cube and Volume of Cuboid has been used. The question says that the metallic rectangular block has been melted to form a single cubical block. Then surely, the volume of initial cuboid will be equal to the volume of cube. Using this concept, let's solve the question.

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★ Question :-

A rectangular metallic block is 50cm*20cm*8cm. if it is melted and reformed into cubical block. Find the length of the edge of the cube.

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★ Formula Required :-

$\: \: \huge{\boxed{\sf{\green{\mapsto \: \: Volume \: of \: Cuboid \: = \: Length(L) \: \times \: Breadth(B) \: \times \: Height(H)}}}}$

$\: \: \huge{\boxed{\sf{\green{\mapsto \: \: Volume \: of \: Cube \: = \: Side^{3}}}}}$

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★ Solution :-

Given,

» Dimensions of the metallic rectangular block = 50 cm × 20 cm × 8 cm

*Here we no need to find what is length, breadth or height. Directly we can calculate its volume which is required.

Now according to the question and using formula, we get,

➮ Volume of cube = Volume of Cuboid

➮ (Side)³ = 50 × 20 × 8

➮ (Side)³ = 8000

$\: \: \huge{\sf{\blue{\Longrightarrow \: \: \: Side \: = \: \sqrt{8000} \: \: = \: 20}}}$

➮ Side of cuboid = 20 cm

$\: \: \underline{\boxed{\rm{\purple{Thus \: the \: length \: of \: edge \: of \: the \: cube \: is \: \underline{20 \: cm}}}}}$

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$\: \: \underline{\boxed{\sf{Confused? \: Don't \: worry \: let's \: verify \: it}}}$

Clearly we know that, Volume of initial metallic block = Volume of Cube.

Here each side of cube is equal, so edge is 20 cm.

So now for verifying, let's simply apply the value of side of cube in equation.

✰ (20 cm)³ = 50 cm × 20 cm × 8 cm

✰ 400 cm² × 20 cm = 1000 cm² × 8 cm

✰ 8000 cm³ = 8000 cm³

Clearly, the equation is satisfied since LHS = RHS. So our answer is correct.

Hence its Verified.

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$\: \: \underline{\boxed{\rm{\orange{\mapsto \: \: Let's \: understand \: more}}}}$

• Volume of Cylinder = πr²h

where r is its radius and h is its height.

• Volume of Cone = ⅓(πr²h)

where r is its radius and h is its height.

• Volume is the amount of air or any other compressible substance present in a three dimensional solid. It is measured in (unit)³.

• CSA (Curved Surface Area) is the measure of the area of a three dimensional solid from its front eye view rejecting the base areas. Its measured in (unit)².

• TSA (Total Surface Area) is the measure of the area of a three dimensional solid from outer view as a whole solid including bases. Its measured in (unit)².

Answer 2

Answer:

Step-by-step explanation:

$\huge{\boxed{\sf{\pink{Answer:-}}}}$

Given that:-

Cuboidal box of dimensions 50 × 20 × 8 cm.

We need to find the edge of cube.

$\boxed{\sf{\pink{Let's \ Do!:-}}}$

This all, is the relation between the volume.

Volume of Cuboid = lbh

• Where l is length
• Where b is breadth
• Where h is height

= 50×20×8 = 8000 $\sf{cm^3}$

Now, volume of cube is a³,so

• a here is the edge or side of cube.

$\huge{\boxed{\sf{\green{a^3=8000}}}}$

$\boxed{\sf{\purple{a= 20}}}$

So, 20 is the answer.