Question

find volume of solid generated by revolving the region bounded by y = √(x) and the lines y = 3 and x = 0 about the x-axis

Answer 1

The formula of finding the volume of the solid generated by revolving the region about x axis is found by multiplying π by the subtraction of integrations of the square of the functions in given interval ;

V=$\int$ π *(f₁(x)²-f₂(x)²)dx. after sketching the graph of the function we can find that the boundary of the solid in x axis [0;9].

integrating in this interval,

V= $\int$₀⁹ π*((3²)-x)dx= π$\int$₀ ⁹(9-x)dx= π*(9x-x²/2)]₀⁹= π*81/2;

the volume of the solid is V=π *81/2