A rectangular box can hold 1,000 pounds of sand when
completely filled. Given that the width of the box is 3
feet and its length is 8 feet, what is the minimum depth,
in feet, of the box to the nearest foot? (Assume that 1
cubic foot of sand weighs 8 pounds.)
F.
6
G.
7
H.
8
J.
9
K.
10
To find the minimum depth of the box, we can start by calculating the volume of the box.
Volume = Length x Width x Depth
Volume = 8 ft x 3 ft x Depth
Volume = 24 ft^2 x Depth
Since the box can hold 1,000 pounds of sand, and 1 cubic foot of sand weighs 8 pounds, the volume of the box in cubic feet must be 1,000 lbs / 8 lbs/ft^3 = 125 ft^3.
Setting the two equations equal to each other:
24 ft^2 x Depth = 125 ft^3
Depth = 125 ft^3 / 24 ft^2
Depth ≈ 5.2 ft
Rounded to the nearest foot, the minimum depth of the box is 5 feet.
Therefore, the nearest answer choice is F. 6.