Question

If the length, breadth and height of one packet of one gross match-box are 2·8 dcm ,1.5dcm and 0·9 dcm respectively, then calculate the volume of one match-box. [one gross = 12 dozen]. But if the length and breadth of one match box be 5 cm and 3·5 cm, then also calculate the height of it.

Answer 1

1 gross = 12 dozen = 144 match - box.
The length of one gross of match - box = 2.8 dcm = 28 cm .
breadth = 1.5 dcm = 15 cm and height =0.9 cm = 9 cm .
`therefore ` volume of jone gross match -box `=28 xx 15 xx 9 cu-cm = 37580 " cc" `
`therefore` volume of one match - box be `= 3780/144 "cc "` =26.25 cm.
Length· of each match box = 5 cm, breadth = 3·5 cm.
Let the height of each match-box be x cm.
So, the volume of each match-box =` 5 xx 3.5 xx x " cc" = 17.5 x " cc "`
`therefore` volume of 144 match boxes `=17.5 x xx 144 " cc" `
`17.5x 144 = 3780 ` or . `x=(3780)/(17.5 xx 144)=1.5 `
Hence the volume of one match-box is 26-25 cc and the height of each match-box is 1 ·5 cm.