Question

A conical cup $18$ cm high has a circular base of diameter $14$ cm The cup is full of water which is now poured into a cylindrical vessel of circular base whose diameter is $10$ cm What will be the height of water in the vessel

• A. $10.7cm$
• B. $11.76cm$
• C. $1176cm$
• D. $1.716cm$

Answer 1

Answer: (B)

$11.76cm$

Radius of the conical cup $r=\frac{14}{2}=7cm$ and height of the cup $h=18cm$ Therefore
Volume of water in the cup $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 18=924c{m}^3$
Now radius of the circular cylinder $R=\frac{10}{2}cm=5cm$
Let the height of water be H centimeters Then
Volume of water $=\pi R^{2}H=\frac{22}{7}\times 5\times 5\times H=\frac{25\times 22}{7}Hcm$
This volume is equal to the volume of water poured out from the cup i.e.
$\frac{22}{7}\times 25H=924orH=\frac{924\times 7}{22\times 25}=11.76cm$
$\therefore$ Height of water in the vessel $=11.76cm$