Question

a metallic sphere of total volume pi is melted and recast into shape of right circular cyclinder of radius 0.5 cm what is height of cyclinder ?

Answer 1

volume of sphere = pi cm cube

4/3pi r3 = pi

4/3 r3 = 1

volume of cylinder = pi r2 h

pi 0.25 h= pi

25h/100 = 1

25h=100

h=100/25=4

height of cylinder = 4 cm

Answer 2

Given:

The volume of metallic sphere=π

The radius of cylinder=0.5cm

To find:

The height of the cylinder

Solution:

The height of the cylinder is 4cm.

We can find the height by following the given process-

We know that the volume of the metallic sphere is equal to the volume of the right circular cylinder.

We are given that the volume of the sphere is π cubic units.

Let the height of the cylinder be h.

So, the volume of the cylinder=π$r^{2}$h

The radius of the cylinder, r=0.5 cm

From the given information,

π$r^{2}$h=π

$r^{2}$h=1

On putting the value of r, we get

$(0.5)^{2}$×h=1

0.25h=1

h=1/0.25

h=100/25

h=4 cm

Therefore, the height of the cylinder is 4cm.