Question

Two dairy owners $A$ and $B$ sell flavoured milk filled to capacity in mugs of negligible thickness, which are cylindrical in shape with a raised hemispherical bottom. The mugs are $14cm$ high and have diameter of $7cm$ as shown in given figure. Both $A$ and $B$ sell flavoured milk at the rate of $Rs.80$ per litre. The dairy owner $A$ uses the formula $\pi r^{2}h$ to find the volume of milk in the mug and charges $Rs.43.12$ for it. The dairy owner $B$ is of the view that the price of actual quantity of milk, should be charged. What according to him should be the price of one mug of milk? Which value is exhibited by the diary owner $B$? (Use $\pi =\frac{22}{7}$)

Answer 1

Let us first find the actual quantity of milk in mug.

Actual capacity of the glass$=$ Volume of cylinder$-$Volume of the hemisphere.

Volume of the cylinder:

Given:diameter$=7$cm, radius$r=\frac{d}{2}=\frac{7}{2}$cm and height$=14$cm.

Volume of cylindrical glass$=\pi r^{2}h=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times 14=539{cm}^3$

Volume of hemisphere$=\frac{2}{3}\pi r^3=\frac{2}{3}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times \frac{7}{2}=\frac{539}{6}{cm}^3$

Actual capacity of the glass$=$Total volume of cylinder$-$Volume of hemisphere.

$=539{cm}^3-\frac{539}{6}{cm}^3=\frac{2695}{6}{cm}^3$

The owner charges Rs.$80$ per liter.

Amount for $1$ liter$=$Rs.$80$

Amount for $1000{cm}^3=$Rs$\frac{80}{100}$ since $1l=1000{cm}^3$

Amount for $1{cm}^3=\frac{80}{100}$

Now, $1$ mug has $\frac{2695}{6}{cm}^3$ capacity.

Amount for $\frac{2695}{6}{cm}^3=\frac{80}{100}\times \frac{2695}{6}=$Rs.$35.93$

$VALUE$:Since owner $B$ is honest, the value exhibited by him is $HONESTY$