Question

A cylindrical tank with a radius of 12 inches and a height of 20 inches is full of water. Does the tank have enough water to fill 250 spherical shaped water balloons if each of the water balloons has a radius of 2 inches? Explain.

Answer 1

The number of balloons that can be filled is approximately 270 so the tank has enough to fill 250 balloons.

Explanation:

Given the Cylindrical tank with a radius(r) of 12 inches and a height(h) of 20 inches

Volume of a Cylinder=
`\pi r^2h`

Volume of Cylindrical tank=
`\pi r^2h=\pi X 12^2 X 20 =9047.8` cubic inches

Radius of 1 spherical shaped balloon= 2 inches

Volume of a sphere =
`=(4)/(3)\pi r^3`

Volume of 1 spherical shaped balloon
`=(4)/(3)\pi r^3=(4)/(3) \pi X2 ^3=33.5` cubic inches

Number of balloons that can be filled =9047.8/33.5=270

Answer 2

Yes, it can.

Explanation:

To know if you can fill all the water balloons with the tank, the first thing is to calculate the volume of each one.

Volume of the tank, is a cylinder, whose volume is given as follows:

Vc = Pi * Rc ^ 2 * h

The radius of the cylinder has a value of 12 inches and the height of 20 inches. Thus:

Vc = 3.14 * (12) ^ 2 * 20 = 9043.2 inches ^ 3

Now, the volume of each globe that is a sphere is given by the following equation:

Ve = (4/3) * Pi * Re ^ 3

Being the radius of the sphere of 2, we have to:

Ve = (4/3) * 3.14 * 2 ^ 3 = 33.5 inches ^ 3

Now to know if you can fill all the balloons, we calculate the volume ratio of the tank and a balloon.

Vc / Ve = 9043.2 /33.5 = 269.95

Therefore, it can fill the 250 balloons because it has the capacity to carry approximately 269 balloons.