Question

A conical cup 18 cm high has a circular base of diameter 14cm. 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

Hint: Try to attempt such questions, by putting the formula directly. Use the formula to find out the volume of the cone that is Volume of Cone $\dfrac{1}{3}\pi {r^2}h$, where r= radius of the cone and h = height of the cone. Then find out the volume of the cylinder and equate both of them.

Complete step by step answer:
According to the given condition in the question, we have to find out the height of water in the vessel
For that, first we have to find out the radius of the conical cup,
Therefore, radius of the conical cup $r = \dfrac{{14}}{2} = 7cm$ and height of the cup h = 18cm
 

So, Volume of water in the cup $\dfrac{1}{3}\pi {r^2}h = \dfrac{1}{3} \times \dfrac{{22}}{7} \times 7 \times 7 \times 18 = 924c{m^3}$
So, we have found the volume of water in the cup that is $924c{m^3}$,
Now, we have to calculate radius of the circular cylinder $R = \dfrac{{10}}{2}cm = 5cm$
Let us assume the height of water is H centimeters. Then,

Volume of water $ = \pi {R^2}H = \dfrac{{22}}{7} \times 5 \times 5 \times H = \dfrac{{25 \times 22}}{7} \times Hcm$
So, we can say that this volume is equal to the volume of water poured out from the cup
$ \Rightarrow \dfrac{{22}}{7} \times 25H = 924$
$ \Rightarrow H = \dfrac{{924 \times 7}}{{22 \times 25}} = 11.76cm$
Therefore, Height of water in the vessel =11.76 cm

So, the correct answer is “Option B”.

Note: Such concepts of Surface Areas and Volumes are very tricky but what you need to do is to keep a track of all the following formulae. Questions based on Volume of a cone required an understanding that it is nothing but the space or the capacity of the cone. A cone is a three-dimensional geometric shape having a circular base that tapers from a flat base to a point called apex or vertex.