Question

if p,x,y are height ,C.S.A and volume of cone respectively ,prove that : 3πyp^3 - x^2p^2 +9y^2 = 0 . please frds answer dedo .

Answer 1

Step-by-step explanation:

First, we need to know that the CSA is π r L, where r is the radius of the base of the cone and L is the slant height, and the volume is (1/3) π r² p, where r is the radius and p is the height.  So

x = π r L  and  y = (1/3) π r² p.

The first term in the stated sum is then

3 π y p³ = π² r² p^4.

The second term is

x² p² = π² r² L² p².

The third term is

9 y² = π² r^4 p².

Before adding them together, notice that the height p, the radius r and the slant height L are related by Pythagoras' Theorem: L² = r² + p².  So the second term is

x² p² = π² r^4 p² + π² r² p^4.

Now we can see what's going to happen when we add them together:

3 π y p³ - x² p² + 9 y²

= π² r² p^4 - ( π² r^4 p² + π² r² p^4 ) + π² r^4 p²

= 0.