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 14 cm high and have diameter of 7 cm as shown in given figure. Both A and B sell flavoured milk at the rate of ` 80 per litre. The dairy owner A uses the formula to π r<sup>2</sup>h find the volume of milk in the mug and charges ` 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 dairy owner B? (Use π = 22/7)

First we need to find the actual quantity of milk in mug and we know about the hemispherical cavity in the mug, so the volume of mug can be given as

Volume of mug = Volume of cylinder – Volume of hemisphere …(i)

To find Volume of cylinder,

Given that, diameter of the mug = 7 cm

⇒ radius = 7/2 = 3.5 cm

And height of mug = 14 cm

Now,

Volume of cylinder = πr²h

=

= 539 cm³ …(ii)

To find Volume of hemisphere,

We know that, radius = 3.5 cm [same radius as the mug, because the hemisphere is carved out from the radius of the mug]

And,

Volume of hemisphere =

=

= cm³ …(iii)

Putting the values obtained in equations (ii) & (iii) in equation (i),

Volume of mug =

= 539 (1 – 1/6)

= 539 (5/6)

= 2695/6 cm³

We know from the question that,

SP of 1 liter = Rs. 80

⇒ SP of 1000 cm³ = Rs. 80 [∵ 1 liter = 1000 cm³]

So, SP of 1 cm³ = Rs. 80/1000

⇒ SP of 2695/6 cm³ =

Thus, according to him price of one mug is Rs. 35.93

Owner A decides to sell the milk at the rate of volume of the whole cylinder although there is a hemispherical cavity in the mug, while Owner B has different views. He wants to sell the milk at its real value. This shows Owner B is honest.