What is the amount of space within the cylinder not taken up by the three tennis balls stored in it?
The volume of the space within the cylinder not taken up by the tennis balls is approximately 72.62 cubic inches.
Calculating the Volume of the Space Within the Cylinder Not Taken Up by the Tennis Balls
The problem provides the following information:
- The height of the cylindrical container is 8 inches
- The radius of the cylindrical container is 1.43 inches
- The circumference of a tennis ball is 8 inches
To begin finding the volume of space within the cylinder not taken up by the tennis balls, we first calculate the total volume of the cylinder using the formula:
V_cylinder = π × r² × h
Substituting the given values, we get:
V_cylinder = π × (1.43 inches)² × 8 inches
Next, we need to calculate the volume of a single tennis ball. The formula to find the volume of a sphere is:
V_sphere = (4/3) × π × r³
Using the given information that the circumference of a tennis ball is 8 inches, we find the radius (r_ball) to be approximately 1.2732 inches. We can then calculate the volume of a single tennis ball:
V_ball = (4/3) × π × (1.2732 inches)³
To find the total volume occupied by the three tennis balls, we multiply the volume of a single tennis ball by 3:
V_total_balls = 3 × V_ball
Finally, the volume of the space within the cylinder not taken up by the tennis balls can be calculated as:
V_space = V_cylinder - V_total_balls
By substituting the calculated values into the formula, we arrive at the answer to the nearest hundredth, which is approximately 72.62 cubic inches.