A milkman was serving his customers using two types of mugs A and B of inner diameter 5 cm to 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.
@Cutie1312 please.....
Answers
163.54 cm³ and 186.44 cm³ are the volumes of the mugs of both types.
Given,
The diameter of mugs A and B = 5cm
The height of mugs A and B = 10 cm
To Find,
The volume of the mugs of both types =?
Solution,
The diameter of mugs A and B = 5cm
The radius of mugs A and B = 5/2 = 2.5 cm
The volume of mug A = Volume of the cylinder – Volume of the hemisphere
The volume of mug A = πr²h - (2/3)πr³
The volume of mug A = π(2.5)²(10) - (2/3)π(2.5)³
The volume of mug A = (3.14)(6.25)(10) - (2/3)(3.14)(15.625)
The volume of mug A = 196.25 - 32.708
The volume of mug A = 163.54 cm³
The volume of mug B = Volume of the cylindrical – Volume of the conic section
The volume of mug B = πr²h - (1/3)πr²h
The volume of mug B = π(2.5)²(10) - (1/3)π(2.5)²(1.5)
The volume of mug B = (3.14)(6.25)(10) - (1/3)(3.14)(6.25)(1.5)
The volume of mug B = 196.25 - 9.81
The volume of mug B = 186.44 cm³
Hence, the volume of mug A is 163.54 cm³ and the volume of mug B is 186.44 cm³.