If h, C and V respectively represent the height, curved surface area and volume of cone, prove that

C2 = (3 pie Vh2 + 9V2) / h2

  • -1
We know V=πr²h/3
=>r²=3V/hπ.........(1)

Now we know

C= πrl=πr(h²+r²)=πr(h²+3V/hπ)[From (1)]

=>C= r(h²π+3V/h)

=>C²= 3V/hπ(h⁴π²+9V²/h²+6Vhπ

=>C²= 3(Vh³π+ 9V³h/π+ 6V²)

Hence proved
  • -5
V= 1/3pie r2 h, 3 v= pie r2 h, pie r= 3 v/rh, r2 = 3 v/pie h C= pie r l , c= 3 v(√h2+r2)/rh C2 = 9v2(h2+r2)/r2h2 C2=9v2(h2+3 v/pie h)/3 v h2/pie h C2= pieh{9 v2 ( pie h× h2 + 3 v)}/ pie h × 3vh2 C2 = 3 vpie h3 + 9 v2/ h2
  • -5
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