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 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 Rs. 80 per litre. The dairy owner A uses the formula πr2h 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 dairy owner B?​

Answer 1

Step-by-step explanation:

d = 7 cm ; r = d / 2 = 7 / 2 cm

h = 14 cm

volume of cylinder = 22 / 7 * ( 7 / 2 )^2 * 14

                               = 11 * 7 * 7 = 539 cm^3

volume of hemisphere = 2 / 3 * 22 / 7 * ( 7 / 2 )^3

                                      = 11 * 7 * 7 / 3 * 2 = 539 / 6 cm^3

actual capacity of mug = volume of cylinder - volume of hemisphere

                                      = 539 - 539 / 6 = 2695 / 6 cm^3

cost of 1 l of mug = Rs 80

1000 cm^3 = Rs 80 ; therefore 1 cm^3 = 80 / 1000

one mug has 2695 / 6 cm^3 of milk .

so , cost of milk in one full mug = 80 / 1000 * 2695 / 6 = Rs 32.93

• Seller B exhibits the value of honesty