Question

The radii of three cylindrical jars of equal height are in the ratio $1:2:3$. Second jar is full with water which is first poured into the first jar. After fiiling the first jar, water is poured into the third jar. Which of the following statements is true ?

• A. Third jar is half full
• B. Third jar is one third full
• C. Third jar is two thirds full
• D. Third jar is four ninths full

Answer 1

Answer: (B)

Third jar is one third full

Let the radii of three jar be $r,2r$ and$3$r
$\therefore$ volume $V_1=\pi r^{2}h$
$V_2=\pi (2r{)}^{2}h=\pi 4r^{2}h$
$V_3=\pi (3r{)}^{2}h=\pi 9r^{2}h$
Then volume of water remained after pouring in to the first jar
$=4\pi r^{2}h-\pi r^{2}h$
$=3\pi r^{2}h$
$=\frac{1}{3}\times V_3$
$\therefore$ third jar is one third full.