Question

if the metallic cylinder of height 4 cm and radius 3cm is melted and cast into a sphere then the radius of sphere is​

Answer 1

Answer:

I hope it will help you!

Answer 2

Given :

• Height of metallic cylinder is 4 cm.
• Radius of cylinder is 3 cm.
• It is melted and casted into a sphere.

To Find :

• Radius of the sphere.

Solution :

Whenever an object is melted and recasted into a new object, the volume of the initial object and the new object so formed is equal.

Here, we have the radius and height of cylinder.

Calculate the volume of the cylinder using the formula.

Formula :

$\large{\boxed{\bold{\purple{Volume_{cylinder}\:=\:\pi\:r^2\:h}}}}$

Here,

• r = radius of cylinder = 3 cm
• h = height of cylinder = 5 cm

Block in the data,

$\sf{Volume_{cylinder}\:=\:\pi\:3^2\:\times\:4}$

$\sf{Volume_{cylinder}\:=\:\pi\:\times\:9\:\times\:4}$

$\sf{Volume_{cylinder}\:=\:\pi\:\times\:36}$

$\sf{Volume_{cylinder}\:=\:36\:\pi}$

Now, volume of cylinder will be equal to the volume of sphere.

$\large{\boxed{\bold{\purple{Volume_{cylinder}\:=\:Volume_{sphere}}}}}$

$\longrightarrow$ $\sf{\:\pi\:r^2\:h\:=\:\dfrac{4}{3}\:\pi\:r^3\:}$

$\longrightarrow$ $\sf{\:36\:\pi\:=\:\dfrac{4}{3}\:\pi\:r^3\:}$

$\longrightarrow$ $\sf{36\:=\:\dfrac{4}{3}\:r^3\:}$

$\longrightarrow$$\sf{\:36\:\times\:3\:=\:4\:r^3\:}$

$\longrightarrow$ $\sf{108\:=\:4\:r^3}$

$\longrightarrow$ $\sf{\dfrac{108}{4}=r^3}$

$\longrightarrow$ $\sf{27=r^3}$

$\longrightarrow$$\sf{^3\sqrt{27}=r}$

$\longrightarrow$ $\sf{r=3}$

$\large{\boxed{\bold{\purple{Radius\:of\:sphere\:=\:3cm}}}}$