Question

Some spherical balls of diameter $2.8\,\text{cm}$ are dropped into a cylindrical container containing some water and are fully submerged. The diameter of the container is $14\,\text{cm}$. Find how many balls have been dropped in it if the water rises by $11.2\,\text{cm}$.

• A. 50
• B. 150
• C. 250
• D. 350

Hint:

Use displacement: rise in cylinder volume $=\pi R^2 h$ equals $n$ times sphere volume $\frac{4}{3}\pi r^3$. The $\pi$ cancels, keeping arithmetic clean.

Answer 1

The Correct Option is B

Step 1: Container radius \(R=7\), ball radius \(r=1.4\), so \(R=5r\). Volume balance: \( \pi R^2h=n\cdot\tfrac{4}{3}\pi r^3 \).

Step 2: Substituting \(R=5r\) simplifies to \( n=\dfrac{75h}{4r} \).

Step 3: Plug in \(h=11.2,\ r=1.4\): \( n=\dfrac{75\times11.2}{5.6}=150 \). \[ \boxed{150} \]