Calculate the volume of the container. Then, calculate the volume of the balls.
About 170 cubic centimeters
Practice makes perfect
We are told that 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. We want to find the amount of space in the container that is not occupied by rubber balls. To do so, we need to find the volume of the container by recalling the formula for the volume of a cylinder.
V_c=Bh
Here, B represents the area of the base and h is the height of the cylinder. The base is a circle, so we can find the area by recalling the formula for the area of a circle.
B=π r^2In our case, the diameter is 6 which means that the radius is 3. Then, we can calculate the base area of the container by substituting r= 3 into the above formula.
We need to find the volume of each rubber ball. To do so, recall the formula for the volume of a sphere.
V_s= 4/3π r^3
Here, r represent the radius of the sphere. In our case, the radius is equal to 3 centimeters. We can substitute this value into the above formula to calculate the volume of the sphere.
Since we have 3 balls, we need to multiply this volume for 3 to find the volume occupied by the rubber balls.
V_b=3(36π) → V_b=108 π
Finally, the space that is not occupied by the balls is equal to the difference between the volume of the container and the occupied by the rubber balls.
