Multiple choice

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 $V=24\pi +x\left(\displaystyle\frac{4}{3}\pi r^3\right)$, 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?

  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The total volume is 96pi. Initial water is 24pi. Available space = 96pi - 24pi = 72pi. Volume of one pebble = (4/3) * pi * 3^3 = (4/3) * pi * 27 = 36pi. Number of pebbles = 72pi / 36pi = 2.

AI explanation

Calculate the remaining volume available for the pebbles by subtracting the water volume from the cylinder volume, which is 96 pi - 24 pi = 72 pi cubic centimeters. Next, find the volume of one spherical pebble with radius 3 cm using V = (4/3) pi r^3, resulting in (4/3) * pi * 27 = 36 pi cubic centimeters. Divide the available 72 pi by the 36 pi volume of a single pebble to find that a maximum of 2 pebbles can be added.

Keep practicing — related questions