Question

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$<b>Spherical Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm., which contains some water. Find the number of marbles that should be dropped in to the beaker, so that water level rises by 5.6 cm$

Answer 1

Hello User!

Question:

Spherical Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm which contains some water. Find the number of marbles that should be dropped in to the beaker, so that water level rises by 5.6 cm.

Solution:⤵️⤵️

Let number of marbles dropped in the beaker be K.

Diameter of the marble➾ 1.4 cm

∴ Radius of a marble = 0.7 cm

Diameter of the beaker = 7 cm

Radius of the beaker = 7/2 cm

Rise in level of water = 5.6 cm

Now,

Volume Of K marble = Volume of water risen

∴ K × 4/3  π r^3 =  π R^2 H

∴ K × 4/3 × (0.7)^3 = (7/2)
^2 × 5.6

∴ K = 7/2 × 7/2 × 56/10 × 3/4 × 10/7 × 10/7 × 10/7

∴ K = 14 × 3 × 100/4 × 7

∴ K = 4200/28

∴ K = 150

Hence, 150 marbles were droppped into the beaker.

Answer 2

volume of each marble = 4/3 πr^3
r=1.4/2= .7

V= 4/3 ×π ×.7×.7×.7


Volume of Beaker = πr^2h
h= 5.6cm r = 7/2cm

V2= π× 7/2×7/2× 56/10

volume of X marbles=Volume of water
X× (4 ×π×7×7×7)/(3×10×10×10) = (π× 7×7×56)/ (2×2×10)

X = 2×75

X= 150

so number of marbles required is 150.
$150$

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