Question

cm and
the diameters of two balls be
cm, find the diameter of the third
2
A measuring jar of internal diameter 10 cm is partially filled with water. Four equal spherical
balls of diameter 2 cm each are dropped in it and they sink down in water completely. What
will be the change in the level of water in the jar ?
I need solutions fast ​

Answer 1

Question :

★A measuring jar of internal diameter 10 cm is partially filled with water. Four equal sphericalballs of diameter 2 cm each are dropped in it and they sink down in water completely. Whatwill be the change in the level of water in the jar ?

Answer :

Using Capital letters for Cylindrical Jug;

D = 10cm ; R = 5cm

and let the level of water is at H height

r = 2cm

Since 4 similar spherical balls are dropped

so,

Volume of 4 spherical balls =

$4 \times \frac{4}{3} \pi {r}^{3}$

$= 4 \times \frac{4}{3} \times {5}^{3}$

$= \frac{16}{3} \times 125\pi$

$= \frac{2000}{3} \pi \: \: {cm}^{3}$

So, the increase in the volume of jug =

$= \frac{2000}{3} \pi$

Let the increase in level be "h" cm

Now,

increase in volume = ${\pi{R}^2h}$

$\frac{2000}{3} \pi = \pi {R}^{2} h$

Cancel π from both sides

$\frac{2000}{3}={5}^{2}×h$

$\frac{2000}{3×25}=h$

$h=\frac{80}{3}cm$