Question

Find the volume of solid generated by rotating the area bounded by x²+y² =36 and the lines x = 0, x = 3 about X -axis. 

Answer 1

Given curve is x²+y²=36 

∴  y ² = 36 -x² 

Required volume V = `|pi int_0^3 "y"^2  "dy"|`

∴ V = `pi int_0^3 (36 - "x"^2) "dx"`

`= pi [36"x" - "x"^3/3]_0^3`

`= pi {[36(3) - 3^3/3] - 0}`

`= pi (108 - 9)`

∴ V = 99 π cubic units.