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 ๐
r
^{
2
}
h
to 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)

This is a question of CBSE Sample Paper - Class 10 - 2017/18.

Question 29
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 ๐r2h to 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? (๐ข๐ ๐ ๐=22/7)
Let us first find actual quantity of milk in mug
Actual capacity of the glass
= Volume of cylinder โ volume of hemisphere
Volume of cylinder
Given diameter = 7 cm
So, radius = r = ๐ท๐๐๐๐๐ก๐๐/2 "=" 7/2
Height = 14 cm
Volume of the cylindrical glass = ๐๐2โ
= 22/7 ร (7/2)^2 ร 14
= 22/7 ร7/2 ร7/2ร 14
= 11 ร 7 ร 7
= 539 cm3
Volume of the hemisphere
Radius of hemisphere = r = 7/2 cm
Volume of the hemisphere = 2/3 ฯr3
= 2/3ร22/7ร(7/2)^3
= 2/3ร22/7ร7/2ร7/2ร7/2
= (11 ร 7 ร 7)/(3 ร 2) = 539/6 cm3
Actual capacity of the glass
= Total volume of cylinder โ volume of hemisphere
= 539 โ 539/6
= (539 ร 5)/6 = 2695/6 cm3
Now,
The Question is - What according to him should be the price of one mug of milk?
The owner charges 80 Rs per liter
Amount for 1 liter = Rs 80
Amount for 1000 cm3 = Rs 80
Amount for 1 cm3 = Rs 80/1000
Now, one mug has 2695/6 cm3 capacity
โด Amount for 2695/6 cm3 cm3 = Rs 80/1000 ร 2695/6
Amount for 1 mug = Rs 35.93
Thus, one mug costs = Rs 35.93
Now, the question is Which value is exhibited by the dairy owner B
Here value is the human values (not any mathematical value)
Since owner B is honest, the value exhibited by him is honesty

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.