# Mensuration-63

### From Homeworkwiki

**The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively.**

**It is melted and recast into a solid circular cylinder of height 10-2/3 cm. Find the radius of the base of the cylinder.**

**Solution:** Let the radius of the base of the cylinder be r,

Therefore, Volume of the right circular cylinder = Π r^{2} h

Here, height h = 10-2/3 cm = 32/3 cm

Hence, Volume of the right circular cylinder

= 22 / 7 x r^{2} x 32/3 cm^{2}

Volume of the spherical shell = 4 Π / 3 {R_{2}^{3} - R_{1}^{3}}

[where, R_{2} is the outer radius and R_{1} is the inner radius of the spherical shell]

= 4 Π /3 {5^{3} - 3^{3}} = 4/3 x 22/7 x (125 - 27) = 4/3 x 22/7 x 98 cm^{3}

Now, 22/7 x r^{2} x 32/3 = 4/3 x 22/7 x 98

=> r^{2} = 4/3 x 98 x 3/32

=> r^{2} = 12.25

=> r = 3.5 cm

Hence, the radius of the base of the cylinder is 3.5 cm