Hello.
The mixed number fraction 15/3 should be multiplied by the fraction 3/15 to equal the required number 1.
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Look at the prime factorization. If all the factors have powers that are multiples of 6, then the number is a square and a cube. If they are multiples of 3, then a cube; if multiples of 2, then a square.
1000 = 2³·5³ . . . . a perfect cube
4 = 2² . . . . a perfect square
120 = 2³·3·5 . . . . none of the above (not a square or a cube)
36 = 2²·3² . . . . a perfect square
100 = 2²·5² . . . . a perfect square
49 = 7² . . . . a perfect square
125 = 5³ . . . . a perfect cube
25 = 5² . . . . a perfect square
No solution because the lines are parallel.
2n+3
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First we need to find the heigh of the soda can be rearanging the volume formula,

. We can make that

We know that V is 36 and radius is half of the diameter, so radius is 2.


h = 2.87
Now, we can use the height to figure out the volume of a cone. The volume of a cone is

R is 2 again and h is 2.87


12.56*.96 = 12.0576
So a cone with a volume of 12.0576 is the largest that will fit into the soda can