Question

If the area of the three adjacent faces of the cuboid are 8cm^2 ,18cm^2 and 25cm^2 . find the volume of the cuboid?​

Answer 1

Answer :-

Here the Area of Square and Volume of Cuboid has been used. According to this, we know that the sides of square are equal and squares arranged in 3-D shape is a cube. Hence, now if those cubes are arranged further, they will form the cuboid. And since its given that these are adjacent faces, then their will show the dimensions of cube.

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★ Formulas Used :-

$\: \: \underline{\boxed{\boxed{\sf{Area \: of \: Square \: = \: (Side)^{2}}}}}$

$\: \: \underline{\boxed{\boxed{\sf{Volume \: of \: cuboid \: = \: Length(L) \: \times \: Breadth(B) \: \times \: Height(H) }}}}$

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★ Question :-

If the area of the three adjacent faces of the cuboid are 8cm²2 ,18cm²2 and 25cm²2 . Find the volume of the cuboid?

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★ Solution :-

Given,

» Area of three adjacent faces of Cuboid = 8 cm² , 18 cm² and 25 cm²

Now using the formula of area of square, we get,

~ For first dimensions :-

⌬ (lb) = 8 cm²

~ For second dimensions :-

⌬ (bh) = 18 cm²

~ For third dimensions :-

⌬ (lh) = 25 cm

Hence area of sides of cuboid are 8 cm², 18 cm² and 25 cm²

Now let's use the formula of Volume of Cuboid :

⌬ Volume of cuboid = Length × Breadth × Height

⌬ lb × bh × lh = 8 × 18 × 25

⌬ (lbh)² = 3600

⌬ lbh = √3600

⌬ Volume of Cuboid = 60 cm³

$\: \: \underline{\boxed{\boxed{\rm{\mapsto \: \: Hence, \: the \: volume \: of \: cuboid \: is \: \underline{60 \: cm^{3}}}}}}$

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

For verification, we need to simply apply the values we got into the equations we formed.

Then, we got the dimensions in cm.

• cm × cm × cm = cm³ = Unit of Volume

So this is correct.

• 8 × 18 × 25 = 3600

=> Volume of cuboid = √3600 = 60 cm³

Here both the conditions satisfy, so our answer is correct.

Hence, Verified.

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$\: \: \huge{\boxed{\rm{More \: to \: know}}}$

• Volume of Cube = (Side)³

• Volume of cylinder = πr²h

where r is the radius and h is the height.

• Volume of Cone = ⅓(πr²h)

• Area of Rectangle = Length × Breadth

• Area of Triangle = ½(Base × Height)

• Area of Parallelogram = Base × Height.

Answer 2

Solution:-Let the length of cube be L,breadth as B and height equals to H

now,

Now,area of first adjacent face(see in diagram)

=L×B

but it is given as 8,so

L×B=8............i)

Area of second adjacent face(shown in diagram)=B×H

but is is gives as 18,so

B×H=18.......ii)

Area of third adjacent face(see in diagram)=H×L

but it is given as 25,so

L×H=25.........iii)

Now,divide i) equation from ii)

we get

L/H=8/18

L/H=4/9......iv)

multiply equation iii) and iv) we get

L^2=4×25/9

L=10/3

Putting value of L in equation i) we get

B=12/5

putting value of B in iii) we get

H=30/4

Now,we know that volume of cubiod equals to L×B×H=10/3 ×12/5 ×30/4=60cm^3

hence volume of cubiod is 60cm^3