35. A milkman was serving his customers using two types of mugs A and B of inner diameter 5 cm
to Mug'A Mug'B'serve the customers. The height of the mugs is 10 cm.
He decided to serve the customers in 'B' type of mug.
(a) Find the volume of the mugs of both types.
(b) Which mathematical concept is used in the above problem?
Answers
Answer:
(a) To find: Volume of both the mugs.
Mug A – Mug A is cylindrical with a hemispherical opening at one of its end.
Let Volume of mug A = VA
Volume of mug A can be expressed as,
Volume of mug A = Volume of cylindrical mug – Volume of the hemispherical opening
It can be written as,
Volume of mug A = Volume of cylinder – Volume of hemisphere
[∵, Volume of cylinder = πr2h and Volume of hemisphere = (2/3)πr3]
[∵, radius(r) = d/2 = 5/2 cm and height(h) = 10 cm]
⇒ VA = 196.25 – 32.708
⇒ VA = 163.54
Hence, volume of mug A is 163.54 cm3
Mug B – Mug is cylindrical with a conic opening at one of its end.
Let Volume of mug B = VB
Volume of mug B can be expressed as,
Volume of mug B = Volume of cylindrical mug – Volume of the conic opening
It can be written as,
Volume of mug B = Volume of cylinder – Volume of cone
[∵, Volume of cylinder = πr2h and Volume of cone = (1/3)πr2hh
⇒ VB = 196.25 – 9.8125
⇒ VB = 186.44
Hence, volume of mug B is 186.44 cm3
(b) The concept being used here is mensuration by finding volumes of the solid figures, as volumes of mug A and mug B are found by using specific formula.
(c) The milkman chose Mug B to serve his customer, this shows his honesty towards his customers as the volume of mug B is 186.44 cm3 while the volume of mug A is 163.54 cm3. Here, he chose the mug having greater volume i.e., B in which much more milk would get filled than mug A.