The weight of a wooden box made of wooden planks with the thickness of 5 cm along with its covering is 115·5 kg. But the weight of the box filled with rice is 880·5 kg. The length-and breadth of inner side of the box are 12 dcm and 8·5 dcm respectively and the weight of 1 cubic dcm rice is 1 ·5 kg. Determine the inner height of the box. Also determine the total expenditure to colour the outside of the box, if the rate is ₹ 1 ·50 per sq-dcm.

Explanation

The weight of the box filled with rice = 880·5 kg
The weight of the empty box= 115.5 kg .
`therefore` the weight of rice = (880.5-115.5)kg = 756 kg
The volume of rice of 1.5 kg = 1 cu - dcm
`therefore ` .,, ,, ,, ,, ,, 1kg `= 1/1.5 ` ,,
`,, ,, ,, ,, ,, 756 kg =1/1.5 xx 756 `
=510 cu-dcm
Let the inner height of the box be x dcm .
`therefore` the inner volume of the box `=12 xx 8.5 xx x ` cu- dcm
` therefore` the inner height of the box = 5 dcm.
The thickness of the wooden plank = 5 cm =0.5 dcm
`therefore` The outer length of the box `=(12 +2 xx 0.5) dcm` = 13 dcm
Breadth `=(8.5 + 2 xx 0.5) dcm ` = 13 dcm
Height =(5+2 xx 0.5) dcm ` = 6 dcm
So, the required expenditure `= ₹ 517 xx 1.50 = ₹ 775. 50 `
Hence the inner height of the box is 5 dcm and the required expenditure = ₹ 775.50