Question

If c,h,v are the curved surface area, height and volume of a cone prove that,3πvh³-c²h²+9v²=0

Answer 1

let pie = ¥

to prove,3¥vh^3 - c^2h^2 +9v^2 .........1

proof,

v= 1/3¥r^2h

c= 1/2(h^2+ r^2)^1/2 ×2¥r

put the value in equation 1

we get,

=3¥×1/3¥r^2h×h^3 -(1/2(h^2+r^2)^1/2 ×2¥r)^2 ×h^2 + 9×(1/3¥r^2h)^2

¥^2×r^2×h^4 -¥^2×r^2×h^4 - ¥^2×r^4×h^2 + ¥^2×r^4×h^2

=0 proved