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How many cubical blocks having volume 27 cu.cm can be fill up a box 12cm long 10cmwide and 8cm high?​

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Answer:

24 blocks

Explanation:

If a cube has side of length a, the volume is given by a³
In other words if the volume is V, then each side = ∛V

The volume of each cubical block = 27 cm³
each block has a side = ∛27 = 3 cm

The box is 12 cm long, 10 cm wide, 8 cm high

If we stack up the blocks we can fit along the length: 12/3 = 4 blocks

Along the width of 10 cm we can fit only 3 blocks since 3 x 3 cm = 9 cm and that leaves only 1 cm so we cannot fit anymore

Along the height we can fit 2 blocks since 2 x 3 cm = 6 cm

(What I am doing above is finding the whole number part when dividing each of the dimensions of the box by the side length of the cube

12/3 = 4

10/3 = 3 1/3; integer part = 3

8/3 = 2 2/3 ; integer part = 2
)

Therefore total number of blocks we can fit in the box

= 4 blocks length-wise x 3 blocks width-wise x 2 blocks height-wise

= 4 x 3 x 2 = 24 blocks

Other info

24 blocks will occupy 24 x 27 = 648 cm³

Volume of the box = 12 x 10 x 8 = 960 cm³

This leaves 960-648 = 312 cm³ of free space

Answer: You can fit 24 blocks

User Parikshita
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