Volumes of Revolution

Front

Volume of solid with base region R enclosed by f(x)=x^2, y=2, and y-axis. Cross section perpendicular to x-axis is a rectangle with height twice the base length.

Back

6.034

Front

Volume of solid with base region R enclosed by f(x)=√3 and g(x)=3/2x, cross sections are isosceles right triangles perpendicular to x-axis.

Back

2.40

Front

Area of region R in the first and second quadrants above y=20/(1+x^2) and below y=2. Round to the nearest thousandth.

Back

37.961

Front

Volume of solid generated when region R (enclosed by f(x)=x^2-1, y=-4, x=0, x=4) is revolved about y=-4.

Back

1158.619

Front

Volume of solid with base R bounded by y=sin(πx) and y=x^3-4x, cross sections perpendicular to x-axis are squares.

Back

9.978

Front

Find the volume of water in the pond given the region R bounded by y=sin(πx) and y=x^3-4x, with depth h(x)=3-x.

Back

8.369

Front

Find the volume of the solid generated when the region R, enclosed by f(x)=x^2+2, y=2, x=0, and x=4, is revolved about the line y=2.

Back

643.398

Front

Volume of solid generated by rotating region enclosed by y=x and y=1/3x^2 about y=4.

Back

42π/5

Front

Volume of solid generated when R (shaded region in the first quadrant bounded by y=4ln(3-x), y=6, x=2) is revolved about y=8.

Back

168.179

Front

In the figure, R is the shaded region in the first quadrant bounded by the graph of y=4ln(3-x), the horizontal line y=6, and the vertical line x=2. The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a square. Find the volume of the solid.

Back

26.266