Question

A sandbox in the shape of a rectangular prism is ½ ft. high and needs to contain at least 42 ft.³ of sand. How would you write an inequality to express the possible area of the base, b, of the sandbox? ___ b

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the inequality expressing the possible area of the base, we first need to determine the volume of the rectangular prism sandbox. The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.

Given that the height is ½ ft and the volume is at least 42 ft³, we can write the inequality:

V ≥ 42

Substitute the formula for volume:

lwh ≥ 42

Since the height is given as ½ ft, we need to solve for the area of the base, which is lw:

lw ≥ 42 / h
lw ≥ 42 / 0.5
lw ≥ 84

Therefore, the inequality expressing the possible area of the base, b, of the sandbox is:

b ≥ 84