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AleksAgata [21]
3 years ago
7

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 fil

l 250 spherical shaped water balloons if each of the water balloons has a radius of 2 inches? Explain.
Mathematics
2 answers:
Reptile [31]3 years ago
8 0

Answer:

Yes, it can.

Step-by-step 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.

Llana [10]3 years ago
6 0

Answer:

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

Step-by-step 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 ==\frac{4}{3}\pi  r^3

Volume of 1 spherical shaped balloon =\frac{4}{3}\pi  r^3=\frac{4}{3} \pi X2  ^3=33.5 cubic inches

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

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