Question

A designer is trying to build the ideal sized fish tank for a customer. It must hold exactly 24 cubic feet of water and can only be 4 feet in height. If the designer increases the width of the fish tank, what must happen to the length of it so that the volume remains the same? A. The length must stay the same. B. The length must decrease. C. The length must increase.

Answer 1

B. The length must decrease

Explanation:

Given;

maximum volume of the tank, V = 24 ft³

maximum height of the tank, h = 4 ft

let the width of the tank = w

let the length of the tank = L

Volume of the tank is given by;

V = Lwh

L = V / (hw)

L = 24 / (4w)

L = 6/w

L is inversely proportional to w; an increase in w (width) will cause a decrease in L (length)

Therefore, If the designer increases the width of the fish tank, "The length must decrease"