Question

select the correct statement in the table.
tennis balls are traditionally sold in a cylinder which contains three balls. the volume of space in the cylinder not occupied by a tennis ball is modeled in the following function, where r is the radius of a tennis ball, in inches.
v = (πr²)(6r) - 4πr³
select the true statement in the table below.
the factor πr² represents the volume of the can
the factor 6r represents the width of the can
the term 4πr³ represents the volume of the three tennis balls
the term (πr²)(6r) represents the volume of one tennis ball

Explanation:

Step1: Recall Volume Formulas

The volume of a cylinder is \( V_{\text{cylinder}}=\pi r^2h \), and the volume of a sphere is \( V_{\text{sphere}}=\frac{4}{3}\pi r^3 \). For three spheres (tennis balls), the total volume would be \( 3\times\frac{4}{3}\pi r^3 = 4\pi r^3 \).

Step2: Analyze Each Statement

• First statement: \( \pi r^2 \) is the area of the base of the cylinder, not the volume. Volume of the can is \( (\pi r^2)(6r) \), so this is false.
• Second statement: The height of the cylinder (can) with three tennis balls (each with diameter \( 2r \), so three have height \( 6r \)) is \( 6r \), not the width (width is \( 2r \), diameter). So this is false.
• Third statement: As calculated, three tennis balls (spheres) have volume \( 3\times\frac{4}{3}\pi r^3=4\pi r^3 \), so this is true.
• Fourth statement: \( (\pi r^2)(6r) \) is the volume of the cylinder (can), not one tennis ball. So this is false.

Answer:

The term \( 4\pi r^3 \) represents the volume of the three tennis balls