Question

A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A metal sphere is now lowered into the water. The size of the sphere is such that when it touches the inner surface, it just gets immersed. The fraction of water that overflows from the conical vessel is :

• A. $\frac{3}{8}$
• B. $\frac{5}{8}$
• C. $\frac{7}{8}$
• D. $\frac{5}{16}$

Answer 1

Answer: (A)

$\frac{3}{8}$

From the similarity of triangles $\frac{8-r}{10}=\frac{r}{6}$
$48-6r=10r$
$r=3$
Fraction of water overflows
$=\frac{Volumeofsphere}{Volumeofcone}$
$=\frac{\frac{4}{3}\pi (3{)}^3}{\frac{1}{3}\pi \left(6{)}^2\right(8)}=\frac{3}{8}$
Hence,the answer is $\frac{3}{8}$