an aluminum sphere of radius 12cm os melted to make a cylinder of radius 8cm find the height of the cylinder
Answers
An aluminium sphere of radius 12 cm is melted to make a cylinder of radius 8 cm. Find the height of the cylinder.
Solution :
Volume of sphere = Volume of cylinder
(4/3) πr3 = πr2h
Radius of sphere = 12 cm
Radius of cylinder = 8 cm
Height of cylinder = h
(4/3) 123 = 82h
h = (4/3) (12⋅12⋅12) / (8⋅8)
h = 36 cm
Question 2 :
Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in which the level of water in the tanks will rise by 21 cm.
Solution :
Quantity of water flowing out = Quantity of water in rectangular tank
Speed of water = 15 km per hour
= 15000 m
Diameter of pipe = 14 cm = (14/100) m
radius of pipe = 7/100
length of rectangular tank = 50 m,
width of tank = 44 m
height of tank = 21 cm = (21/100) m
Area of cross section ⋅ Time ⋅ Speed = l ⋅ w ⋅ h
πr2 ⋅ Time ⋅ 15000 = (50) ⋅ (44) ⋅ (21/100)
(22/7) ⋅ (7/100)2 ⋅ Time ⋅ 15000 = (50) ⋅ (44) ⋅ 21
Time = (50⋅44⋅21⋅100⋅100⋅7)/(15000⋅100⋅7⋅ 7⋅22)
time = 2 hours