Question

The volumes of a cube and a cuboid ar equal.
If the dimensions of the cuboid ar 18 cm, 12
and 8 cm the edge of th cube is
(A) 8 cm
(C) 12 cm
(B) 10 cm
(D) 16 cm​

Answer 1

$\\ \\ \large\underline{ \underline{ \sf{ \red{given:} }}}$

• Volume of cuboid = Volume of cube

• Dimensions of cuboid are 18cm , 12cm and 8cm.

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}}$

• Edge of cube having same volume as cuboid.

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

We know ,

$\\ \bigstar\boxed{ \bf \: volume \: of \: cuboid = l \times b \times h}$

Here ,

• l = 18cm
• b = 12cm
• h = 8cm

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Putting values we get...

→ Volume of cuboid = 18 × 12 × 8

→ Volume of cuboid = 1728cm³

♠ Volume of cuboid = Volume of cube

Hence , Volume of cube = 1728cm³

$\\ \bigstar \boxed{ \bf \: volume \: of \: cube = {edge}^{3} }$

→ 1728 = edge³

→ edge = 12cm

Hence , edge of the cube is 12cm.

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♦ MORE TO KNOW :-

• Volume of cuboid = πr²h

• Volume of cone = (1/3)πr²h

• Volume of sphere = (4/3)πr³

• Volume of hemisphere = (2/3)πr³

Answer 2

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

The volumes of a cube and a cuboid ar equal. If the dimensions of the cuboid ar 18 cm, 12 and 8 cm the edge of th cube is

(A) 8 cm

(C) 12 cm✔️

(B) 10 cm

(D) 16 cm