Question

The volume of cube and cuboid are equal if the dimensions of the cuboid are 18 12 and 8 the edge of cube will be

Answer 1

Answer:

12 cm

Step-by-step explanation:

Given :-

Volume of cube = Volume of cuboid

Length of cuboid = 18cm

Breadth of cuboid = 12cm

Height of cuboid = 8cm

To find :-

Edge of cube

Using Formula :-

Volume of cuboid = l × b × h

Volume of cube = edge³

Solution :-

Length of cuboid = 18cm

Breadth of cuboid = 12cm

Height of cuboid = 16cm

Volume of cuboid = 18cm × 12cm × 16cm

= 1728cm³

Therefore,

Volume of cuboid = 1728cm³

It is given that,

Volume of cuboid = Volume of cube

1728cm³ = edge³

edge = 12cm

Therefore,

Edge of cube = 12cm

Answer 2

Solution

Given :-

• The volume of cube and cuboid are equal
• dimensions of the cuboid are 18 ,12 and 8.

Find :-

• edges of cube.

Explanation

Using Formula

$\boxed{\tt{\red{\:(Volume_{cube}\:=\:(Side)^3}}}$

$\boxed{\tt{\pink{\:Volume_{cuboid}\:=\:(Length\times Breadth\times Height)}}}$

According to question,

==> Volume of cube = Volume of cuboid

keep required values,

==> (Side)³ = (18 × 12 × 8)

keep in small factor of 18, 12, 8 .

For 18,

• 18 = 2 × 3 × 3

For, 12

• 12 = 2 × 2 × 3

For, 8

• 8 = 2 × 2 × 2

So, Now keep all above Values

==> Side³ = ( 2 × 3 × 3 ) × (2 × 2 × 3) × (2 × 2 ×2)

==> side³ = ( 2 × 2 × 2 × 2 × 2 × 2) × (3 × 3 × 3)

==> Side³ = (2³ × 2³ × 3³)

We Know,

If, a^m = b^n, then a = b.

So, We get

==> Side = 2 × 2 ×3

==> Side = 12

Hence

• Side ( edge) of cube will be = 12 units .

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