Question

From a rectangular wooden piece of 16 cm length,12 cm wide and 8 cm thick at least how many cubes can be made of equal volume whose number. Is a whole number

Answer 1

Answer:

at least 3

Step-by-step explanation:

Given that,

length of rectangular wooden piece = 16 cm

width of rectangular wooden piece = 12 cm

thickness of rectangular wooden piece = 8 cm

Formula to use

v = L x W x T

  = 16 x 12 x 8

 = 1536 cm³

Cubes have equal sides l³

largest cube of integer which is divisible by 1536 is 8

1536/8x8x8 = 1536/512 = 3

Answer 2

Answer:

At least - 24 cubes

Step-by-step explanation:

Rectangular wooden piece

Length = 16 cm

Width = 12 cm,

Thickness = 8 cm

Weneed to divide the piece in cubes with equal volume with side as a whole number.

This is possible only when, all the three dimensions of the piece are exact multiple of the dimension of the side of the cube.

∴ Maximum whole number, common between 8, 12 and 16 = 4

∴ Cube with side = 4 cm can be cut from the rectangle.

NUmber of cubes cut = Volume of the rectangular piece ÷ Volume of the cube

∴ Number of cubes = (16 × 12 × 8) ÷ (4 × 4 × 4)

Number of cubes cut = 24