Question

A cylindrical container of three rubber balls has a height of 18 centimeters and a diameter of 6 centimeters. each ball in the container has a radius of 3 centimeters. find the amount of space in the container that is not occupied by rubber balls. round your answer to the nearest whole number

Answer 1

You have 3 spheres inside a cylinder like for a can of tennis balls. Notice the radius of the cylinder is 3 cm, the same as the radius of the spheres, so the spheres just fit width wise, and 3 spheres height would be 6 radius lengths or 18, which is the same as the cylinder height, so the three spheres are packed to the best fit.

The volume not occupied by the spheres will be the total cylinder volume take away the three spheres volumes.

The cyinder volume with height h=18 and radius r=3 will be approx..
$V cyl= \pi r^2h = \pi *3^2*18 = 508.7 ~cm^3$

The volume of 3 spheres with radius r=3 will be
$3*V sph=3* \frac{4}{3} \pi r^3=3* \frac{4}{3} \pi *3^3=339.12~cm^3$

The volume unoccupied by the spheres inside the cylinder is the difference in those two volumes..
508.68 - 339.12 = 169.56  or 170 cubic centimeters