An aquarium is building a tank in the shape of a right rectangular prism to house large saltwater animals. The volume of space available is 125,000 cubic feet. The aquarium must build a tank that holds no less than 100,000 cubic feet of water. The base can be anywhere from 45–55 feet wide. The height is 50 feet. Which of the following shows a possible dimension for the length of the base?
Let's denote the length of the base as L.
The volume of a rectangular prism is given by the formula V = L x W x H, where V is the volume, L is the length, W is the width, and H is the height.
Given that the volume available is 125,000 cubic feet and the tank must hold at least 100,000 cubic feet of water, we have:
100,000 ≤ L x W x 50 ≤ 125,000
Since the base can be anywhere from 45–55 feet wide, the width W can range from 45 to 55 feet.
Let's first substitute the smallest possible width (45 feet) into the inequality:
100,000 ≤ L x 45 x 50 ≤ 125,000
100,000 ≤ 2250L ≤ 125,000
100/2250 ≤ L ≤ 125,000/2250
L ≥ 44.44
Now, let's substitute the largest possible width (55 feet) into the inequality:
100,000 ≤ L x 55 x 50 ≤ 125,000
100,000 ≤ 2750L ≤ 125,000
100/2750 ≤ L ≤ 125,000/2750
L ≥ 36.36
Therefore, a possible dimension for the length of the base is L ≥ 44.44 feet or L ≥ 36.36 feet.