if a marble of radius 2.1 cm is put into a cylindrical cup full of water of radius 5 cm and height 6 cm, then how much water flows out of the cylindrical cup?
Answers
Step-by-step explanation:
Given :
radius of marble = 2.1 cm
radius of cylinder= 5 cm
height of cylinder= 6cm
To find :
volume of water displaced (flows out) , when the marble is placed in the cylindrical cup.
Formula :
Volume of sphere=4/3πr^3
Volume of cylinder = πr^2h
water displaced = volume of sphere
Solution:
Volume of marble=4/3×22/7×(2.1)^3
=4/3×22/7×2.1×2.1×2.1
=4/3×22/7×21/10×21/10×21/10
=4×22×21×21×1/10×10×10
=88×441/1000
=38,808 /1000
=38.808 cm^3
~38.81 cm^3
therefore,
Volume of spherical marble =38.81 cm^3 ...... (1)
Volume of Cup = 22/7× (5)^2×6
= 22/7×25×6
=22/7×150
= 3,300/7
= 471.428 cm^3
~471.43 cm^3
therefore,
Volume of cylindrical cup = 471.43cm^3
Water displaced= 38.81 cm^3
1cm^3 = 1/1000 litres
therefore,
38.81 cm^3 = 38.81 /1000litres
= 0.03881 litres
~ 0.04 litres
therefore,
0.04 litres of water is displaced when the spherical marble is placed in the cylindrical cup full of water.
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