Find the volume of the solid obtained by rotating the region enclosed by the graphs of , y=15-x, y-3x-5 and x=0 about the y-axis.

Answer 1

15 - x = 0; x = 15; 3x - 5 = 0, x = 5/3; 15 - x = 3x- 5; x = 5, y = 10

Volume by shoder method V = π∫₀¹⁰[(15 - y)² - (y + 5)²/9]dy = π∫₀¹⁰(8y²/9 - 280y/9 + 2000/9)dy =

π/9(8y³/3 - 140y² + 2000y)₀¹⁰ = π/9( 8000/3 - 14000 + 20000) = 26000π/27 = 3025.24