Question

Heya!!!!


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.



- Quality Answer needed​

Answer 1

${\tt{\blue{\underline{\underline{\huge{Answer}}}}}}$

Given:-

➩ Diameter of marble = 1.4 cm

➩ Diameter of beaker = 7 cm

To find:-

➩ Number of marbles in beaker so that the water rises by 5.6cm

____________________

Answer:-

✔Diameter of marble = 1.4 cm

$✔ Radius \: of \: marble \: will \: be = \frac {1.4}{2}$

$✔Volume \: of \: one \: marble \: will \: be = \frac{4}{3} \pi \: r^{2}$

$✔ \: \frac{4}{3} \times \pi \times (0.7) \:^{3}-----\: (1)$

______________________

➩ Diameter of beaker = 7cm

$➩ Radius \: of \: beaker = \: \frac{7}{2} = 3.5cm$

➩ Height of the beaker is 5.6cm

➩ Volume of water = πr²h = π x (3.5)² x 5.6-----(2)

_______________________

No of marbles dropped in the beaker will be

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

$➩ \: \frac{\pi \times (3.5) ^{ 2}\times 5.6}{ \frac{4}{3} \times \pi \times (0.7)^{3}}$

So the number of marble dropped = 150

---------------------------------------

Hence 150 marbles have been dropped in the breaker.