6. 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.
Both A and B sell flavoured milk at the rate of Rs 80 per lit. The dairy owner
A uses the formula tor2h 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. Understanding the case answer the
following question.
a.What is the volume of the mug without raised hemispherical bottom?
i.548 cu cm
ii. 539 cu cm
iii. 546 cu cm
iv. 523 cu cm
b. What is the volume of the raised hemispherical bottom?
i. 539/6 cu.cm
ii. 537/5 cu cm
iii. 546/5 cu cm
iv.436/6 cu cm
c.What is the actual capacity of mug?
i. 2695/7 cu cm
ii. 2687/6 cu cm
iii. 2695/6 cu cm
iv. 2573/5 cucm
d. What according to him should be the price of the mug of milk?
i. Rs. 35.93
ii. Rs 37.74
ii. Rs 32.58
iv. Rs 30.56
e.How much more he is charging?
Rs 7.20
Rs 5.45
Rs 5.55
Rs. 6.70
Answers
Answer:
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=7cm, radiusr=
2
d
=
2
7
cm and height=14cm.
Volume of cylindrical glass=πr
2
h=
7
22
×
2
7
×
2
7
×14=539cm
3
Volume of hemisphere=
3
2
πr
3
=
3
2
×
7
22
×
2
7
×
2
7
×
2
7
=
6
539
cm
3
Actual capacity of the glass=Total volume of cylinder−Volume of hemisphere.
=539cm
3
−
6
539
cm
3
=
6
2695
cm
3
The owner charges Rs.80 per liter.
Amount for 1 liter=Rs.80
Amount for 1000cm
3
=Rs
100
80
since 1 l=1000cm
3
Amount for 1cm
3
=
100
80
Now, 1 mug has
6
2695
cm
3
capacity.
Amount for
6
2695
cm
3
=
100
80
×
6
2695
=Rs.35.93
VALUE:Since owner B is honest, the value exhibited by him is HONESTY