Question

If h, C, V are respectively the height, the curved surface area and volume of a cone, then 3πV³ – C²h² + 9V² is equal to

(a) 0 

(b) 1 

(c) 2 

(d) 3

Answer 1

Answer: (a) = 0

C = πrl =  \(\pi r\sqrt{h^2+r^2}\)  and V =\(\frac{1}{3}\pi r^2 h\)    where, r and l are respectively the radius of the base and slant height of the cone.

∴  3πVh³ – C²h² + 9V² = 3π  × \(\frac{1}{3}\pi r^2 h\) ×h³ – π²r²(h²+r²)h² + 9 × \(\frac{1}{9}\pi^2 r^4 h^2\)  

 = π²r²h⁴ – π²r²(h²+r²)h² – π²r⁴h² = 0.