Answer :

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 = πr^{2}h

=

= 539 cm^{3} …(ii)

To find Volume of the 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,

The volume of hemisphere =

=

= cm^{3} …(iii)

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

The volume of mug =

We know from the question that,

SP of 1 liter = Rs. 80

⇒ SP of 1000 cm^{3} = Rs. 80 [∵ 1 liter = 1000 cm^{3}]

So, SP of 1 cm^{3} = Rs. 80/1000

⇒ SP of 2695/6 cm^{3} =

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**.

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