Volume (V=BH)

Question

A cylindrical tube contains 5 spherical ball bearings.  The tube is 20 centimeters long and has a diameter of 4 centimeters.  Each ball bearing in the tube has a radius of 2 centimeters.  Find the amount of space in the tube that is not occupied by ball bearings.  Round you answer to the nearest cubic centimeter.

Answer 1

Hello Denise. Let's find out how much space the tube has without the ball bearings. As you mentioned, the formula for volume is Volume=Base times Height. Because the base of a cylinder is a circle, finding the area of the base is (pi)(r^2). Given the diameter is 4, then radius is 2. (pi)(2^2) times 20 would give you the volume of the tube.

 

Now you need to take away the space that is occupied by the ball bearings. The ball bearings are spherical shaped, volume of a sphere is calculated by (4/3)(pi)(r^3). Given the radius of them is 2cm, plug in 2 as r. And there are five of them, so don't forget to multiply the volume by five. And then subtract the volume of the five ball bearings from the volume of the tube to find the amount of the space is left.