1. Tennis balls with a diameter of 6.6 cm are sold in cans of three. The can is a cylinder. What is the volume of the space NOT occupied by the tennis balls?

Question

To find the volume of the space not occupied by the tennis balls, we first need to find the volume of the can and then subtract the volume of the three tennis balls.
Volume of the can:
The can is a cylinder, so we use the formula for the volume of a cylinder:
V_can = πr^2h
Where r is the radius of the can (half the diameter) and h is the height of the can.

Given that the diameter of the tennis ball is 6.6 cm, the radius is 6.6/2 = 3.3 cm.
Let's assume the height of the can is equal to the diameter of the tennis ball, so h = 6.6 cm.

Therefore,
V_can = π(3.3)^2(6.6)
V_can = π(10.89)(6.6)
V_can = 226.7 cm^3

Volume of three tennis balls:
The volume of one tennis ball can be calculated using the formula for the volume of a sphere:
V_ball = (4/3)πr^3
V_ball = (4/3)π(3.3)^3
V_ball = (4/3)π(35.937)

Since there are three tennis balls in the can, the total volume of all three would be:
V_total_balls = 3 * (4/3)π(35.937)
V_total_balls = 3 * 47.916 π
V_total_balls = 143.748 π cm^3

Now, to find the volume of the space not occupied by the tennis balls:
V_space = V_can - V_total_balls
V_space = 226.7 - 143.748 π
V_space ≈ 226.7 - 450.207
V_space ≈ 223.5 cm^3

Therefore, the volume of the space not occupied by the tennis balls is approximately 223.5 cm^3. 2. Explain how you could get a formula for the volume of the solid.

Answer 1

To get a formula for the volume of the solid, you first need to determine the shape of the solid and then find a formula that relates the dimensions of the solid to its volume.

For example, if the solid is a cylinder, the formula for the volume of a cylinder is V = πr^2h, where r is the radius of the base of the cylinder and h is the height of the cylinder.

If the solid is a sphere, the formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere.

If the solid is a rectangular prism, the formula for the volume of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height of the prism.

By identifying the shape of the solid and understanding the relationship between the dimensions of the solid and its volume, you can derive a formula that calculates the volume of the solid.