Question

The conical glass in the figure shown below is fixed with soft drink upto the brim.The quantity of soft drink required to fill $30$ such glasses is

A. $3.8L$
B. $3.85L$
C. $4.5L$
D. $2.56L$

Answer 1

We have the figure of conical glass which is filled with soft drink. For this they have mentioned the height of the glass and radius of the glass. The height of the glass is from the center point of the glass and radius of the glass. For this we have to find out the quantity of soft drink required.

Complete step by step answer:
From the given we have the height of the glass and radius of the glass, based on this information we are going to find out the volume of the glass.
That means the volume of the cylinder is, $V = \dfrac{1}{3}\pi {r^2}h$.
Where $\pi = 3.14$
Radius, $r = 3.5\,cm$ and
Height, $h = 10\,cm$
By substituting all the values in the volume of the cylinder we get,
$V = \dfrac{1}{3} \times 3.14 \times {\left( {3.5} \right)^2} \times 10 \\\ \Rightarrow V = \dfrac{{384.65}}{3} \\\ \Rightarrow V = 128.21 \\\$
We calculated the volume of cylinder, now we are going to calculate the quantity of soft drink required to fill $30$ glasses,
Required quantity to fill glasses = volume of the cylinder $\times$ $30$ glasses
$\text{Required quantity to fill glasses}= 128.21 \times 30 \\\ \therefore \text{Required quantity to fill glasses}= 3846.3$
Now we are converting the above value in to liters that means, $1L = 1000\,ml$
Now we get the required soft drink in liters $= 3.85L$

Thus the correct option is B.

Note: For finding the required quantity of the soft drink for $30$ glasses first we have to find the volume of glass based on the volume of the cylinder formula for calculating the volume we have all the required data. After calculating the volume we find the required quantity. After finding the required quantity we have converted the value into liters.