Question

please solve this question ​

Answer 1

$\orange{ \mid{ \underline{ \overline{ \tt Number \: of \: marbles \: dropped \: in \: the \: beaker (n) = 150}} \mid}}$

Given:

spherical marbles of diameter 1.4 cm each are dropped into a cylindrical beaker of radius 3.5 cm containing some water.

Some marbles dropped into the beaker so that water level in the beaker rises by 5.6cm

To find:

Number of marbles dropped in the beaker

Explanation:

i ) Diameter of the each spherical marble (d) = 1.4cm

Radius (r) = d/2 =1.4/2 = 0.7cm

Let the number marbles dropped in the beaker = n

ii) Radius of the cylindrical

beaker (R) = 3.5 cm

after dropping some marbles

level raised in the beaker (H)= 5.6cm

iii) n × volume of each sperical

marble = Volume of raised water in the cylindrical portion

=> n × (4/3)πr³ = πR²H

=> n = (πR²H)/[(4/3)πr³]

= (3R²H)/(4r³)

= [3×(3.5)²×5.6]/[4×(0.7)³]

= [3×3.5×3.5×5.6]/(4×0.7×0.7×0.7)

After cancellation, we get

= 150

Therefore,

Number of marbles dropped

in the beaker (n) = 150

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