A sandbox in the shape of a rectangular prism is 1/2ft. 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
To find the volume of a rectangular prism, you multiply the length by the width by the height. In this case, the height is given as 1/2 ft. and the volume is given as at least 42 ft.³.
So, the volume of the sandbox can be expressed as:
Volume = b * w * 1/2 ≥ 42
b * w * 1/2 ≥ 42
To find the inequality for the possible area of the base, we need to isolate b since we're looking for the base area.
b * w * 1/2 = 42
b * w = 84
b = 84 / w
Therefore, the inequality to express the possible area of the base, b, of the sandbox is:
b ≥ 84 / w