Question

Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter
7 cm containing some water. Find the number of marbles that should be dropped
into the beaker so that the water level rises by 5.6 cm.

Answer 1

Given:-

• diameter of marble = 1.4cm

Therefore,

• radius = $\frac{1.4}{2}$ = 0.7cm
• diameter of cylinderical beaker = 7cm.

To find:-

• the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm.

step-by-step solution:-

Volume of 1 marble = $\frac{4}{3}$πr³

• => $\frac{4}{3}$ × π × (0.7)³---------(1)

Now,

• Diameter of beaker= 7cm

Therefore,

• radius of beaker = $\frac{7}{2}$

= 3.5cm

• Height of water = 5.6cm

Volume of water = πr²h

• => π × (3.5)² × 5.6 ------------(2)

Now,

No. of marbles dropped =

$\frac{volume\:of\: water\:marble}{volume\:of\:1 \:marble}$

from equation (1) and (2)

• ⇒ No.of marbles dropped =

• ⇒$\frac{π × (3.5)² × 5.6}{4/3 × π × (0.7)³}$

• ⇒ No. of marbles dropped = 150

Hence , 150 marbles have been dropped in the beaker.

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hope it helps u buddy : )

• Explaination with diagram ; refer to attachment↑↑

Answer 2

Answer:

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Step-by-step explanation:

Diameter of each marble = 1.4 cm

Radius of each marble = 0.7cm

Volume of each marble = $\frac{4}{3}\pi r^3 = \frac{4}{3} \times (0.7)^3\:cm^3$

The water rises as a cylinder column

Volume of cylindrical column filled with water = $\pi r^2h = \pi \times(\frac{7}{2} )^2 \times 5.6\:cm^3$

Total number of marbles = $\frac{Volume\:\:of\:\: cylindrical \:\:water \:\:column}{Volume\:\:of \:\:marble}$

$=\frac{\pi \times (\frac{7}{2})^2 \times5.6 }{\frac{4}{3} \times (0.7)^3}\\\\=\frac{7\times7\times5.6\times3}{2\times2\times4\times0.7\times0.7\times0.7}\\\\= 150$