Question

13. A solid metallic sphere of diameter 6cm is melted and cast to a solid cylinder of
radius 3cm. Find the height of the cylinder.

Answer 1

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

$\sf{Height \ of \ cylinder \ is \ 4 \ cm}$

$\sf\orange{Given:}$

$\sf{For, \ sphere}$

$\sf{\implies{Diameter (d)=6 \ cm}}$

$\sf{For, \ cone}$

$\sf{\implies{Radius (R)=3 \ cm}}$

$\sf\pink{To \ find:}$

$\sf{Height(h) \ of \ cylinder.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Radius(r) \ of \ sphere=\frac{Diameter}{2}}$

$\sf{\therefore{Radius (r)= \frac{6}{2}}}$

$\sf{\therefore{Radius (r)=3 \ cm}}$

$\sf{Cone \ is \ formed \ by \ melting \ the}$

$\sf{sphere, \ hence \ they \ will \ have}$

$\sf{same \ volume.}$

$\boxed{\sf{Volume \ of \ Sphere=\frac{4}{3}\times\pi\times \ r^{3}}}$

$\boxed{\sf{Volume \ of \ Cylinder=\pi\times \ R^{2}\times \ h}}$

$\sf{\therefore{\frac{4}{3}\times\pi\times3^{3}=\pi\times3^{2}\times \ h}}$

$\sf{\therefore{h=\frac{4\times3\times3\times3}{3\times3\times3}}}$

$\sf{h=4 \ cm}$

$\sf\purple{\tt{\therefore{Height \ of \ cylinder \ is \ 4 \ cm}}}$

Answer 2

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

A solid metallic sphere of diameter 6 cm is melted and recast a solid cylinder of radius 3 cm.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The height of the cylinder.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Solid metallic sphere of diameter = 6 cm

Solid metallic sphere of radius = 6cm/2

Solid metallic sphere of radius = 3 cm

Solid cylinder of radius = 3 cm

Using the formula of the volume of sphere and volume of cylinder :

A/q

$\longrightarrow\rm{\frac{4}{3} \pi r_1^{3} =\pi r_2^{2} h}\\\\\\\longrightarrow\rm{\dfrac{4}{3} \times (3)^{3} \times \pi =\pi \times (3)^{2} \times h}\\\\\\\longrightarrow\rm{\dfrac{4}{\cancel{3}} \times\cancel{ 27} \times \cancel{\pi} = \cancel{\pi }\times 9\times h}\\\\\\\longrightarrow\rm{4\times \cancel{9} = \cancel{9} \times h}\\\\\\\longrightarrow\rm{\pink{h=4\:cm}}$

Thus;

The height of the cylinder will be 4 cm .