Question

A block of wood is 75 cm × 50 cm × 40 cm. How many cubes of side 0.1 m can be carved out of it?

Answer 1

Find out how much of cubes of side 0.1 m can be carved out of it .

To prove

Formula

Volume of a cube = a³

where a is the sides of a cube.

As given

Sides of a cube is 0.1m

As

1 meter = 100 cm

sides of a cube in cm = 0.1 × 100

= 10 cm

put in the formula

Volume of a cube = 10 × 10 × 10

= 1000 cm³

As Given

A Block of the wood is 75cm × 50cm × 40cm .

But as volume of the cube is the multiple of 10 .

thus we take dimensions of the wooden block be 70cm × 50 cm × 40 cm ( instead of 75cm × 50cm × 40cm ) than the volume of the wooden block become the multiple of 10.

Formula

Volume of the wooden block = Length × Breadth × Height

Put the value

Volume of the wooden block = 70 × 50 × 40

= 140000

Let us assume that the number of cubes curved out be x.

Volume of the wooden block = x × volume of cube

140000 = x × 1000

`x =(140000)/(1000)`

x = 140

Therefore the number of cubes curved out from the wooden block are 140.

Answer 2

150 cubes of side 0.1 m can be carved out of it.

Explanation:

Given a block of wood is
`75 cm * 50 cm * 40 cm`

i.e, Volume of block of wood =
`150,000 cm^3`

Convert
`150,000 cm^3` in
`m^3`

Use conversion:
`1 cm^3 = 0.000001 m^3`

then,

`150,000 cm^3` =
`150,000 * 0.000001 =0.15 m^3`

so, the volume of block of wood =
`0.15 m^3`

Cube of side 0.1 m have the volume =
`0.1 * 0.1 * 0.1 = 0.001 m^3`

then,

Number of cubes =
`(Volume of block of wood)/(volume of cube)`

∴ number of cubes =
`(0.15)/(0.001) = (15 * 1000)/(1 * 100) =150`

therefore, 150 cubes of side 0.1 m can be carved out of it.