Question

a metalic sphere of diameter 30 cm is melted and recast into a cylinder of radius 10 cm.find height of the cylinder.
​

Answer 1

Given :

• Diameter of metallic Sphere is 30 cm.
• Radius of Cylinder is 10 cm .

To Find :

• Height of Cylinder .

Solution :

$\longmapsto\tt{Radius\:of\:Sphere=\cancel\dfrac{30}{2}=15\:cm}$

$\longmapsto\tt{Radius\:of\:Cylinder=10\:cm}$

Now ,

Volume of Cylinder = Volume of Sphere :

$\longmapsto\tt{{\cancel{\pi}}{{r}^{2}h}=\dfrac{4}{3}{\cancel{\pi}}{{r}^{3}}}$

$\longmapsto\tt{{r}^{2}h=\dfrac{4}{3}{r}^{3}}$

$\longmapsto\tt{10\times{10}\times{h}=\dfrac{4}{3}\times{15}\times{15}\times{15}}$

$\longmapsto\tt{100h=4\times{5}\times{15}\times{15}}$

$\longmapsto\tt{100h=4500}$

$\longmapsto\tt{h=\dfrac{45{\cancel{00}}}{1{\cancel{00}}}}$

$\longmapsto\tt\bf{h=45\:cm}$

So , The Height of Cylinder is 45 cm...

_______________________

• C.S.A of Cylinder = 2πrh
• T.S.A of Cylinder = 2πr(r+h)
• Volume of Sphere = πr²h
• Surface Area of Sphere = 4πr²
• Volume of Sphere = 4/3 πr³

_______________________