Question

olive has an aquarium full of water and fish. her aquarium is 24 in long and 12 in wide. she bought a cylindrical bag of new fish in water. if her bag has a diameter of 5 inches and the water is 7.5 inches high in the bag, how much will it raise the level of the tank when she pours it in?

Answer 1

To calculate how much the water level will rise in the tank, we need to calculate the volume of water in the cylindrical bag and add it to the volume of water in the tank.

The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the cylinder and h is its height.

In this case, the diameter of the bag is 5 inches, so the radius is 5/2 = 2.5 inches. The height of the water in the bag is 7.5 inches.

So, the volume of water in the bag is V = π(2.5)^2(7.5) = 147.26 cubic inches (rounded to two decimal places).

The volume of water in the tank is the length times the width times the height, which is 24 x 12 x h, where h is the height by which the water level will rise.

We can set up an equation to solve for h:

24 x 12 x h + 147.26 = 24 x 12 x h'

where h' is the final height of the water level in the tank.

Simplifying the equation, we get:

h' = (24 x 12 x h + 147.26) / (24 x 12) = h + 0.51

Therefore, the water level in the tank will rise by approximately 0.51 inches when Olive pours the water from the bag into the tank.