You are building a dresser in the form of a rectangular prism that must be 48 inches tall with a volume of 4320 cubic inches..

Question

The length and width each must be less than 2 feet. Which of the following dimensions are the possible width and length of the cabinet?

1. 9 inches by 10 inches
2. 10 inches by 10 inches
3. 6 inches by 20 inches
4. 5 inches by 18 inches
5. 2 inches by 45 inches

Answer 1

The volume of a rectangular prism (a "box" shape) is given by:

V = l•w•h where "l" = length, "w" = width, and "h" = height

We are given V and h so we can plug those into our equation:

4320 = l•w•48

Now we can divide both sides by 48 to get:

90 = l•w

So we need to pick choices where the length times the width equals 90. 9 inches times 10 inches equals 90 so that works. 5 inches times 18 inches equals 90 so that works. 2 inches times 45 inches equals 90 so although that works, it doesn't meet the requirement that the dimensions be under 2 feet (24 inches).

Answer 2

V = L * W * H = 4320 in³

H = 48 in

L * W = V / H = 4320 in³ / 48 in = 90 in²

Which of the following dimensions are the possible width and length of the cabinet?

1. 9 inches by 10 inches: Correct because L * W = 90 in²
2. 10 inches by 10 inches: Incorrect because L * W = 100 in²
3. 6 inches by 20 inches: Incorrect because L * W = 120 in²
4. 5 inches by 18 inches: Correct because L * W = 90 in²
5. 2 inches by 45 inches: Incorrect since each dimension must be less than 2 feet (24 inches)