Question

If H, C and V are respectively the height, curved surface area and volume of a cone, then what is 3πVH³ + 9V² equal to?
1. C²H²
2. 2 C²H²
3. 5 C²H²
4. 7 C²H²

Answer 1

Correct Answer - Option 1 : C²H²

Given:

H is the height of the cone

C is the curved surface area of the cone

V is the volume of the cone

Formula used:

The volume of cone = (πr²H/3)

The curved surface area of cone = πrl

Calculation:

Now we have to find the value of 3πVH3 + 9V2 

⇒ 3V(πH³ + 3V)

Now, we substitute the value of V

⇒ 3 × (1/3) × πr² × H(πH³ +  3 × (1/3) × πr²× H)

⇒ πr2H(πH3 + πr2H)

⇒ π²r2H²(H² + r2)

⇒ π²r²l²H²

⇒ C²H²

∴ The value of 3πVH3 + 9V2 is C2H2