Question 33
IntegrationFind the volume of the solid of revolution generated when the region bounded by y = 3x2, x = 0, x = 2 and x-axis is rotated about the x-axis through 360°. [Take π = 22/7]
- A.178 unit3
- B.180 unit3
- C.181 unit3
- D.190 unit3
Show the answer and explanation
Answer: C (181 unit3)
Explanation
V = π∫₀² (3x²)² dx = π∫₀² 9x⁴ dx = π × 9 × 32/5 = 288π/5 ≈ 181 unit³.