Question

lfe,tand v are curved surface area, total surface area and volume of a cylinder then show that th ch 4v8 rh where r and hare radius and height​

Answer 1

Given :

For A cylinder

The curved surface area = c

The total surface area = t

The volume = v

To Proved :

t h² = c h² + 4 v² + 8 v² r h

Answer 2

$\bold{ANSWER≈}$

If C, T and V are curved surface, total surface area and volume of a cylinder then prove that th^2 = ch^2 + 4v^2+ 8V^2 rh if r is radius and h is height?

If C,T and V are the curved surface area, total surface area and volume of a cylinder, prove that Th2=Ch2+4V2+8V2rh.

This cannot be proved since the equation to be proved is dimensionally inconsistent.

The dimensions of both Th2 and Ch2 are L4M0T0 whereas the dimensions of 4V2 and 8V2rh are L6M0T0 and L8M0T0 respectively.

What can be proved is that Th2=Ch2+2Vh.

C=2πrh,T=2πrh+2πr2 and V=πr2h.

⇒LHS=Th2=(2πrh+2πr2)h2=2πrh3+2πr2h2, and,

RHS=Ch2+2Vh=2πrh3+2πr2h2=LHS.