Question

Julia needs to make a box in the shape of a rectangular prism with a height of 3 inches and a volume of 243 cubic inches. The dimensions, in inches, must be whole numbers greater than 1. Julia claims that the length and the width must be equal.

Part A: What dimensions would support Julia's claim about the length and with of the box?
Part B: What dimensions would not support Julia's claim about the length and width of the box.
Part A length =______________
Part A width=_____________________.
Part B length_________________
Part B Width=_____________________.

Answer 1

The volume of a rectangular prism is equal to length*width*height. In this case, we have V = 243 and H = 3.

243 = LW(3), so LW = 81, where L & W are whole numbers greater than 1. There are only 3 possible pairs of values for this: 27 x 3, 9 x 9, and 3 x 27 (we cannot use 1 x 81 or 81 x 1, since we need dimensions > 1).

Part A: This could be true if Length = 9 in and Width = 9 in, as 9 x 9 = 81.

Part B: The claim could be false if Length = 27 in and Width = 3 in, as 27 x 3 = 81, but 27 is not equal to 3.

Note that the width cannot be longer than the length.