Question

Small pebbles are continuously being added to a graduated cylindrical container containing water. The total volume of water and pebbles can be represented by the equation $V=24\pi +x\left(\frac{4}{3}\pi r^3\right)$, if the pebbles are considered to be spheres of radius $r$. If the volume of the graduated cylinder is $96\pi$ cubic centimetres, then, what is the maximum number of pebbles with a radius of $3$ centimetres that can be added without the volume of the fluid exceeding that of the graduated cylinder?

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (B)

$2$

Volume of cylinder $=$ Volume of water $+$ pebbles

$\Rightarrow 96\pi =24\pi +x\times \frac{4}{3}\pi r^3\Rightarrow x\times \frac{4}{3}\pi \times 3\times 3\times 3=72\pi$

$\Rightarrow x=\frac{72}{36}=2$