Question

A wooden cuboid is 24 cm by 30 cm by 36 cm cubes of equal side are cut from all its corner .the volume of the remaining block is 20088 cm cube what is the length of the age of each cube cut off from the cuboid




please explain the answer​

Answer 1

Given -

• Dimensions of cuboid = 24 cm × 30 cm × 36 cm

• Volume of remaining block = 20088 cm³

To find -

• The length of each cube.

Solution -

Volume of cuboid = L × B × H

Where,

L = length

B = Breadth

H = Height

On substituting the values -

Volume of cuboid = L × B × H

Volume of cuboid = 24 × 30 × 36 cm

Volume of cuboid = 25920 cm³

Since a cuboid has 8 corners, that mean 8 cubes are being cut.

Let the side of cube be x cm

Volume of cube = a³

Where,

a = side of cube

According to Question -

Volume of 1 cube = x³

Volume of 8 cubes = 8x³

Volume of remaining block = 20088cm³

That means,

25920 - 8x³ = 20088

8x³ = 25920 - 20088

8x³ = 5832

So,

x³ = 5832/8

x³ = 729

x = ³√729

x = 9cm

$\therefore$ The edges of each cube will be 9 cm.

_______________________________________

Answer 2

Dimensions of cuboid = 24 cm × 30 cm × 36 cm

Volume of remaining block = 20088 cm³

To find -

The length of each cube.

Solution -

Volume of cuboid = L × B × H

Where,

L = length

B = Breadth

H = Height

On substituting the values -

Volume of cuboid = L × B × H

Volume of cuboid = 24 × 30 × 36 cm

Volume of cuboid = 25920 cm³

Since a cuboid has 8 corners, that mean 8 cubes are being cut.

Let the side of cube be x cm

Volume of cube = a³

Where,

a = side of cube

According to Question -

Volume of 1 cube = x³

Volume of 8 cubes = 8x³

Volume of remaining block = 20088cm³

That means,

25920 - 8x³ = 20088

8x³ = 25920 - 20088

8x³ = 5832

So,

x³ = 5832/8

x³ = 729

x = ³√729

x = 9cm

\therefore∴ The edges of each cube will be 9 cm.