A can of tennis balls has an inside diameter of 7 cm and height of 20 cm if the diameter of a tennis ball is 6 cm how much space in the tennis ball can is not occupied by the three balls?

Answer 1

Well, let's first calculate the volume of the can.

So, we would use πr2 to find the area of its base, so if 7 is the diameter, 3.5 is the radius, or r.

Assuming 3.1415 for π, 3.5 * 3.5 = 12.25. 12.25*3.1415 = 38.483375.

Now, we multiply this by the height, so 38.483375*20=769.6675.

Then, we will calculate the volume of each tennis ball, each has a radius of 3, being that they have a diameter of 6, as the diameter is twice of the radius.

To calculate the area of a tennis ball, we will use the formula 4/3πr3, using again 3.1415 for pi, and 3 for r. 33 equals 27, this multiplied by 3.1415 is 84.8205, then this multiplied by 4/3 is 113.094.

Now, we have our volumes, the cylinder or can is 769.6675 cm3 and our balls are each 113.094 cm3, which we will multiply by three because there are three balls in the can, giving us 339.292 cm3, which is the total volume that the tennis balls take up.

Now, we simply find what percent of 769.6675 339.292 is.

So, we will divide 339.292 by 769.6675 to get approximately 0.440829319, which me multiply by 100 to get a percent, giving us 44.0829319, which is the percent of the can that the tennis balls take up.