Amita wants to make a mold for a candle.she wants the shape of the candleto be a rectagular prism with a volume of exactly 23 cubic centimeters. She want the sides to be whole centimeters.how many different moldcan she make?

The volume of a rectangular prism is l x w x h (length x width x height). 23 is a prime number, meaning that its only factors are 23 and 1. Therefore, if you want three integers to multiply together to form 23, the only possibility is 23, 1, and 1 (in any order).

That last statement in parentheses is what makes this question ambiguous. This is a pet peeve of mine, and I'd like to slap whoever wrote it. If she was making bricks, for example, there would be no difference what dimension she chose to be height, length, or width. A brick from a 23 x 1 x 1 mold would be indistinguishable of a brick from a 1 x 23 x 1 mold or a 1 x 1 x 23 mold (note that the numbers are in different orders). Therefore, the answer would be that she could make only one mold. This is probably the answer that your teacher is expecting.

However, if you know how to make candles (which has basically NOTHING to do with learning math), you know that the candle's wick comes out of the top of the mold. That means she could make one mold that was 23 cm high, and 1 cm wide and long (i.e. a tall skinny candle), and she could make a second mold that was only 1 cm high and 1 cm long, but 23 cm wide (i.e. a short, really wide candle). The third possibility, with a height and width of 1 cm, and length (a.k.a. depth) of 23 cm would result in a short, skinny, really deep candle. However, in my opinion, once removed from the mold the second and third option would be indistinguishable from each other. So I would say the real answer is that she could make two different molds.

Unfortunately, your teacher can argue that the answer is only one mold, or that it's two, or that it's three. This is why I HATE stupid ambiguous questions like this! They only serve to confuse the students who are supposed to be learning. You could be the best mathematician on the planet, and you're still reduced to having to read the mind of whoever wrote the question.[/soapbox]

Kudoes, JCaron. I couldn't agree more.

I tried giving you a rep, but it will not let me. Some silliness about "spreading it around". I don't know how to take that:)

Thanks! :D