2020 · Q66
If H, C and V are respectively the height, curved surface area and volume of a cone, then what is 3πVH³ + 9V² equal to?
Elementary MathematicsMensuration
- AC²H²
- B2C²H²
- C5C²H²
- D7C²H²
Explanation
3*pi*V*H^3+9V^2 = 3V(pi*H^3+3V) = 3*(pi*r^2*H/3)*pi*H*(H^2+r^2) = (pi*r*l)^2*H^2 = C^2*H^2. Hence option (A). Using C = pi*r*l and V = pi*r^2*H/3, both sides reduce to pi^2*r^2*l^2*H^2.