Question

A cylinder of radius 12cm contains water up to the height 20cm.A spherical iron ball is dropped into the cylinder and thus water level is raised by 6.75cm.what is the radius of ball?

Answer 1

$\huge\underline\mathrm{Question-}$

A cylinder of radius 12 cm contains water up to the height 20cm. A spherical iron ball is dropped into the cylinder and thus water level is raised by 6.75 cm. What is the radius of ball?

$\huge\underline\mathrm{Answer-}$

Radius of spherical ball is 9 cm.

$\huge\underline\mathrm{Solution-}$

$\begin{lgathered}\bold{Given} \begin{cases}\sf{Radius\:of\:cylinder\:(r)\:=12\:cm} \\ \sf{Water\:level\:raised\:upto\:height=\:6.25\:cm}\end{cases}\end{lgathered}$

To find :

• Radius of spherical ball.

Solution :

Let the radius of spherical ball be " $r_1$ "

★ According to the question :

Volume of cylinder = volume ot spherical ball

: $\implies$ πr²h = $\dfrac{4}{3}$ π ${r_2}^{3}$

★ Putting the given values :

: $\implies$ $\cancel{\pi}$ × (12)² × 6.75 = $\dfrac{4}{3}$ × $\cancel{\pi}$ × r³

: $\implies$ $\dfrac{144\:\times6.75\:\times\:3}{4}$ = r³

: $\implies$ r³ = 729

: $\implies$ r = $\sqrt[3]{729}$

: $\implies$ r = 9

$\therefore$ Radius of spherical ball is 9 cm.

Answer 2

Question :--- A cylinder of radius 12cm contains water up to the height 20cm.A spherical iron ball is dropped into the cylinder and thus water level is raised by 6.75cm.what is the radius of ball ?

Formula and Concept used :---

→ The Spherical ball will rise the Water level Equals to its volume ...

So, we can say that,

→ Volume of Rise of water level = Volume of spherical ball .

→ Volume of cylinder = π*r²*h

→ Volume of Sphere = 4/3 * π * r³

______________________________

❁❁ Refer To Image First .. ❁❁

Given :--

• Radius of cylinder = 12cm.
• Rise of Water level = 6.75cm = Height of cylinder which was Affected due to spherical ball.
• Let Radius of Spherical ball = r cm.

Comparing both Volume now , [ as told above ] .

→ π * r² * h = 4/3 * π * (r)³

Putting values ,

→ π * (12)² * 6.75 = 4/3 * π * (r)³

π will be cancel from both sides ,

→ (12)² * 6.75 = 4/3 * (r)³

→ 3 * 12 * 12 * 6.75 = 4 * (r)³

Dividing both sides by 4 now,

→ 3 * 3 * 12 * 6.75 = (r)³

→ 3 * 3 * (3 * 4) *(3* 2.25) = (r)³

→ (3 * 3 * 3) * (2.25 * 4) * 3 = (r)³

→ (3 * 3 * 3) * ( 3 * 3 * 3) = (r)³

Cube root both sides now ( one term will come out From three ).

→ 3 * 3 = r

→ r = 9 cm.

Hence, radius of Spherical ball will be 9cm.