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*3, 9*9, and 3*27 (we cannot use 1*81 or 81*1, since we need dimensions > 1).
Part A. This could be true if Length = 9 in and Width = 9 in, as 9*9 = 81.
Part B. The claim could be false if Length = 27 in and Width = 3 in, as 27*3 = 81, but 27 is not equal to 3.
*Note that the width cannot be longer than the length.

Answer 2

Part A.
 sqrt 81 = 9; L = 9 ; W = 9 inches

Part B.
if length =27 , width =3, though 27*3 = 81 but then 27 is not equal 3. So false