Open Middle®
Directions: A rectangular prism has a volume of 144 cubic units and a base of 48 square units. What could the possible dimensions be?
Hint
How can my understanding of factors help me solve this problem?
Answer
There are a several possible dimensions that fit this criteria.
One possible answer is 8 x 6 x 3
One possible answer is 8 x 6 x 3
Source: Stem Savvy Girls
6,8,3
6,8,3
replying to myself
6,8,3
8,6,and 3
3x6x8 or 8x6x3
3,6.and 8
8 6 and 3
1x48x3
8 6 and 3
12x4x3
24x2x3
[24×2]x3
[12×4]x3
(12 x 4) x 3
(You do not need the brackets)
(2^4 x 3^2)
(This is what I used)
8 x 2 x 9
3 x 6 x 8
In the integers:
length × width × height = 1×48×3, 2×24×3, 3×16×3, 4×12×3 and 6×8×3, as well as all their permutations.
In the rational numbers, there are an infinite number of solutions. The height has to be 3, because volume = base * height => 144 = 48 * h, but the rectangle that is the base with an area of 48 square units can have any length a and width b = 48/a.
8x6x3
8x6x3
It is 6 x 8 x 3
There might be smth else but idk
12x12x4
that doesn’t work 12×12 is 144
(12×4)x3
OK FINE! 1x1x144
ahh I missed out. 6*8*3
6,8,3
4 by 12 by 3 is also possible.
6,8,and 3
4 by 12 by 3 can also be used and is a possible solution.