Q ) A solid in the form of a cone of height h, mounted on the top of a solid - Maths - Surface Areas and Volumes

Question

Q ) A solid in the form of a cone of height h, mounted on the
top of a solid right circular cylinder of height 1/3 h The
circumference of the base of the cone and that of the cylinder are
both equal to C If V be the volume of the solid then prove that
C = 4 X square root of 3 pie V / 8 h
Urgently need the answer to the above
question

Manmeet Singh · Accepted Answer

The height of cone = h

The height of cylinder = $\frac{h}{3}$

The radius of both the cone and cylinder are equal = r (since circumference are equal, radii are equal)

We have to prove:

$C = 4 \sqrt{\frac{3 π V}{8 h}} = \sqrt{\frac{16 \times 3 π V}{8 h}} = \sqrt{\frac{6 π V}{h}}$

The solution is:

$C = 2 π r r = \frac{C}{2 π}$

Volume of solid = volume of cone + volume of cylinder

$V = \frac{1}{3} π r^{2} h + π r^{2} \times \frac{h}{3} \Rightarrow V = \frac{2 π r^{2} h}{3} \Rightarrow V = \frac{2 π (\frac{C}{2 π})^{2} h}{3} \Rightarrow V = \frac{C^{2} h}{6 π} \Rightarrow C^{2} = \frac{6 π V}{h} \Rightarrow C = \sqrt{\frac{6 π V}{h}}$