Case Study Based Question from Surface Areas and Volumes
Ram observes that a juice seller is having a cylindrical vessel of base radius 25 cm and height 40 cm and it is full of juice. He is selling the juice in small cylindrical glasses of diameter 10 cm and height 10 cm.
Based on the above information answer the following questions :
(i) If the bigger cylindrical vessel is closed, then find the total surface area of the vessel. [2 Marks]
(ii) Find the number of small glasses that can be filled with juice from the bigger vessel. [2 Marks]
Doubt by Saksham
Solution :
Dimensions of Cylindrical Vessel
R = 25 cm
H = 40 cm
Dimensions of each Small Cylindrical Glass
r = 10/2 = 5 cm
H = 10 cm
i) Total Surface area of Bigger Cylindrical Vessel = 2πR(H+R)
= 2(22/7)(25)(40+25)
= (22/7)(50)(65)
= 71500/7
= (22/7)(50)(65)
= 71500/7
= 10214.28 cm²
ii) Number of small Glasses that can be filled with juice from the bigger vessel
= (Volume of juice in Bigger Vessel)/(Volume of Juice in each small glass)
=πR²H/πr²h
=R²H/r²h
=[(25)²×40]/[(5)²×10]
=[625×4]/25
=25×4
=100
=R²H/r²h
=[(25)²×40]/[(5)²×10]
=[625×4]/25
=25×4
=100
Hence, 100 small glasses can be filled from the bigger cylindrical vessel.