Math, asked by ammxu, 9 months ago

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

Answered by burhaanikIQ
8

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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