Question

A cylindrical tennis ball container can contain maximum three balls stacked on one another. The top and bottom balls also touch the lid and the base of the container respectively. If the volume of a tennis ball is \( 240 \text{ cm}^3 \), then what is the volume of the container?

• A. \(1080 \text{ cm}^3\)
• B. \(840 \text{ cm}^3\)
• C. \(1440 \text{ cm}^3\)
• D. \(720 \text{ cm}^3\)

Hint:

For container problems, understand the geometry. Volume of container differs from total volume of individual objects inside. Convert spherical to cylindrical using formulas.

Answer 1

The Correct Option is A

Step 1: Volume of 1 ball is given
Volume of 1 tennis ball = \(240 \text{ cm}^3\) Step 2: Total number of balls stacked = 3
Since the container contains 3 balls stacked vertically and all touch each other and the ends, the container must hold the volume equal to the volume of all 3 balls. \[ \text{Volume of container} = 3 \times \text{Volume of 1 ball} = 3 \times 240 = 720 \text{ cm}^3 \] Wait! But this is the volume occupied by the **balls only**, not the volume of the **cylindrical container**. Key Concept:
Each ball is spherical, and the container is cylindrical. The balls are stacked such that the cylinder’s height is equal to \(3 \times \text{diameter of ball}\), and the cylinder's radius is equal to the radius of one ball. Let’s calculate volume using the cylindrical formula: \[ V = \pi r^2 h \] But we don’t know \(r\) and \(h\), so instead we’ll assume the radius from the sphere. Let radius of ball = \(r\)
Volume of one ball = \(\frac{4}{3} \pi r^3 = 240\) Step 3: Find radius from sphere volume: \[ \frac{4}{3} \pi r^3 = 240 \Rightarrow r^3 = \frac{240 \times 3}{4 \pi} = \frac{720}{4\pi} = \frac{180}{\pi} \] Now volume of cylinder: \[ V = \pi r^2 h = \pi r^2 \cdot 6r = 6 \pi r^3 \] Substitute \(r^3 = \frac{180}{\pi}\): \[ V = 6 \pi \cdot \frac{180}{\pi} = 6 \times 180 = 1080 \text{ cm}^3 \] \[ \boxed{1080 \text{ cm}^3} \]