the region in the first quadrant bounded on the left by the circle x^2+y^2=3 on the right by the line x=sqrt3 and above by the line y=sqrt3, about the y axis

Question

find the volume of the solid

Answer 1

To solve this problem, we will use the washer method for vertical axis rotation

π∫_a^b R²-r² dy where:

Outer Radius --> R = √3 <-- area is below the line y=√3

Inner Radius --> r = √(3-y²) <-- area is above the curve x=√(3-y²)

Bounds --> 0≤y≤√3 <-- a=0 and b=√3

Calculation

π∫₀^√3 [(√3)²-(√(3-y²))²] dy

= π∫₀^√3 [3-(3-y²)] dy

= π∫₀^√3 y² dy

= π[(√3)³/3]

= π[√(27)/√9]

= π√3

Hope this helped!