# Maths

Amita wants to make a mold for a candle. She wants the shape of the candle to be rectangular prism with a volume of exactly 28 cubic cm.
The answer for this question is given as 10 molds. Can you explain in detail how the answer is 10 to better understand.

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1. What the question does not say, but what I will assume is true to have your answer of 10, is that the dimensions must be whole numbers.
Otherwise there would be an infinite number of cases

So we need 3 multipliers (LWH) to get 28
the factors of 28 in triples are
1 1 28
1 2 14
1 4 7
2 2 7

now each one of these can be turned to have a different base

e.g. the first one can be arranged only 2 ways, that is , a base of 1 or a base of 28
Same is true of last one, but the 2nd and 3rd can each have 3 different bases

so:
factors-- number of ways

1 1 28 -- 2
1 2 14 -- 3
1 4 7 --- 3
2 2 7 --- 2

total number of ways = 2+3+3+2 = 10

I hope this makes sense to you

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2. 10

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3. 10

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4. 10000000

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5. 10

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6. sorry I meant 10

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7. 10 molds

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8. 10

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