Question

Amita wants to make a mold for a candle. She wants the shape of the candle to be a rectangular prism with a volume of exactly 28 cubic centimeters. She wants the sides to be in whole centimeters. How many different molds can she make?

Answer 1

Answer & Step by Step Explanation:

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