SOLUTION: if I have 68 sugar cubes that are 1cm by 1cm by 1cm, will they fit in my cup that has a radius of 4cm and height of 8cm?

Question 1008540: if I have 68 sugar cubes that are 1cm by 1cm by 1cm, will they fit in my cup that has a radius of 4cm and height of 8cm?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
volume of the cup = pi * r^2 * h = pi * 4^2 * 8 = pi * 16 * 8 = pi * 128 = 402.1238 cubic cm.

the volume of the 68 sugar cubes is 1 * 1 * 1 * 68 = 68 cubic cm.

if you melted them so that they became liquid, they should fit in the coffee cup no problem.

if you kept them as cubes, then you should be able to fit them as follows:

with a radius of 4, the cup has a diameter of 8.

this is assumed to be the inner dimension of the cup.

the diameter of 8 becomes a diagonal of 8 within a square.

the square that would fit into that circle would have a maximum side measure of 2s^2 = 8^2 which becomes 2s^2 = 64 which becomes s^2 = 32 which becomes s = sqrt(32).

maximum side measure = sqrt(32) = 5.656 cm.

you could fit 25 cubes on each row within the cup.

they would measure 5 * 5 = 25 square cm.

25 square cm is equal to 25 cubes of sugar.

they would be 1 cm high.

the cup is 8 cm high, so the cup could fit 25*8 = 200 of them.

since you only have 68 of them, you can fit them very easily with plenty of room to spare.

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