A cylindrical pencil of 2 cm diameter is sharpened to produce a perfect hemispherical portion at one end...

Question

A cylindrical pencil of 2 cm diameter is sharpened so as to produce a perfect hemispherical portion at one end and a perfect conical portion of length 2 cm at the other end.

Find the volume of Pencil.

Answer 1

Volume of Sphere - 4/3 Pi r^3
=> Volume of Hemisphere - 2/3 Pi r^3

Volume of Cone - 1/3 Pi r^2 h
since h=2cm r=1cm (dia 2cm)
so h=2r
=> 2/3 Pi r^3

Total Volume of Pencil -
4/3 Pi r^3

r=1cm
Pi=3.14

Total Volume of Pencil (tip and back as middle portion is not given) -
4/3 * 3.14 * 1
=> 4.18

Answer 2

d=2cm so r=d/2=1cm
h=2cm

Volume of cylinder=pi*r^2*h
Volume of cone=1/3*pi*r^2*h
Therefore
Volume of shavings=2/3*pi*r^2*h
=2/3*3.14*1^2*2
=4.186cm^3