A case of 42cm x 42cm x 60cm, I want to put tins which are 6cm in dia & 12 cm high?

Question

What is the max number of tins that fit in the case ?
(Kindly explain the steps of thinking, thank you)

Answer 1

I will assume that the measurements of the case are the inside measurements and that the measurements of the tins are the outside measurements.

This in mind you will be able to fit 7 tins in each direction in the case for a total of 49 tins per layer. You will also be able to fit a total of 5 layers inside the case. This brings your total number of tins to 245 tins.

The question is how many tins fit in the case and not how many tins could you empty into the case therefore a volume calculation does not work here.

Answer 2

lets make the case 60 x 42 and 42 high.

We can put 10 x 7 on each layer and can fit 3 layers getting us 210

We now have a 6 cm gap on the top where we can put our cans in sideways.

It is 60 x 42 so we can put 5 x 7 in this layer =35

Total 245

We can also look at putting the cans in offset rows.

The first row has 7 cans the second 6 each row is 5.196 apart centre to centre. This is putting them across the 42cm diameter

We have 60cm to put them in. How many rows can we fit?

6+(x-1)*5.196<=60 5.196(x-1) =54 so x can be at most 10 so we can have 11 rows in all

We have 6 rows with 7 cans and 5 rows of 6 =72 cans per layer

We can have 3 layers =216 cans plus the top layer as before

35 giving 251 cans as a maximum

Answer 3

It would be nice to pack the bottom layer hexagonally with rows of 7 tins and 6 tins alternately, four times, making 52 tins in the layer. Five of those layers would get you 260 tins in the case.

Unfortunately, although the centres of those rows are only 5.196 cm apart, the width of 8 of them is not 8 * 5.196 = 41.57 cm, which would have worked, but (6 + 7 * 5.196) = 42.37 cm, so you cannot do it after all. Stay with 245.

Answer 4

The volume of the case is 105,840 cubic centimeters:
(42 X 42 X 60 = 105,840)

To obtain the volume of the tins use the following formula:
pi X radius squared X height of the tin
(3.14 X 9 X 12 = 339.12)

Divide the volume of the case by the volume of each tin to determine how many will fit.

105,840/339.12 = 312.1

Therefore, 312 tins should fit in the case.

Answer 5

Volume of case
=42*42*60 cm^3
=105840cm^3.......1]
Volume of tin
=PI*r^2*h
=22/7*3^2*12
=339.428cm^3.......2]
no of tins
=1]/2]
=311.818
approx 312
note...some volume will be lost
since box is a cross section and
tins are round

Answer 6

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Answer 7

the volume of the case 42 * 42 * 60 = 105,840
the volume of the tin : 6^2 * pi /4 * 12 =339
105,840 % 339 = 312 ( 105,840 div 339 = 312)
so the answer is 312

Answer 8

maximum no of tins (assuming there is no interstitial space
=volume of the case/vol of 1 tin
=42*42*60/3.14*3^2*12
=312 tins

Answer 9

area of case = length*breath*height
=42*42*60
=105840 cm3

area of one tin = 6*12
=72
tins fitted =105840/72
=1470

Answer 10

Depends purely on what you can carry. Waste of time filling the box if you can't pick the box up.