Question

$\red {8}$
A solid metallic Sphere of radius 42 cm is melted and cast into small solid cylinders of radius 7 cm and height 3 cm .
Find how many such cylinders formed .​

Answer 1

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

$\tt Given \begin{cases} \sf{Radius \: of \: metallic \: sphere \: is \: 42 \: cm.} \\ \sf{Radius \: of \: cylinder \: is \: 7 \: cm.} \\ \sf{Height \: of \: cylinder \: is \: 3 cm.}\end{cases}$

_____________________________

To Find :

$\hookrightarrow \sf{How \: many \: cylinders \: can \: form \: when \: sphere \: is \: meleted}$

_____________________________

Solution :

We have to find the cylinder formed when sphere is melted. So,

We will find the radius of the sphere then Volume of one cylinder and then devide volume of sphere by volume of one cylinder.

$\rule{150}{2}$

$\large{\star{\underline{\boxed{\sf{Volume \: = \: \frac{4}{3} \pi r^3}}}}}$

$\sf{ \rightarrow \: volume = \frac{4}{3} \times \frac{22}{7} \times ({42})^{3} } \\ \\ \sf{volume = \frac{4}{3} \times \frac{22}{ \cancel7} \times \cancel{74088}} \\ \\ \sf{volume = \frac{4}{ \cancel3} \times 22 \times \cancel{10548}} \\ \\ \sf{volume = 88 \times 3528} \\ \\ \sf{volume = 310464 \: {cm}^{3} }.......(1)$

$\large{\star{\underline{\boxed{\sf{Volume = 310464 \: cm^3}}}}}$

$\rule{200}{2}$

$\large{\star{\underline{\boxed{\sf{Volume \: = \: \pi r^2 h}}}}}$

$\sf{volume = \frac{22}{7} \times ( {7)}^{2} } \times 3 \\ \\ \sf{volume = \frac{22}{ \cancel{7}} \times \cancel{ 49} \times 3} \\ \\ \sf{volume =66 \times 7 } \\ \\ \sf{volume = 462 \: {cm}^{3}......(2)}$

$\large{\star{\underline{\boxed{\sf{Volume = 462 \: cm^3}}}}}$

$\rule{200}{2}$

Devide equation 1 by 2.

No. of cylinders = 310464/462

No. of cylinders = 672

$\large{\star{\underline{\boxed{\sf{Number \: of \: cylinders = 672}}}}}$

$\rule{200}{2}$

#answerwithquality

#BAL

Answer 2

$\huge{ \mathfrak{ \overline{ \underline{ \underline{ \red{ Answer☻}}}}}}$

THANKS FOR ASKING SUCH A QUESTION DEAR FRIEND ☺️✌️