Calculate Volume

Find the volume of the solid generated by revolving the area bounded by y = x² and the x-axis from [0, 2] around the x-axis. 

• 8π/3

• 32π/5

• 108π/5

• 16π/3

Find the volume of the solid generated by revolving the area bounded by y = x² and the x-axis from [0, 2] around the y-axis. 

• 8π

• 6π

• 2π

• 0

Find the volume of the solid of revolution obtained by rotating the region in bounded by y = x³ + 1, x = 1 and y = 1 about the y-axis.

• 11π/3

• 4π/13

• 3π/7

• 2π/5

What is the volume of the solid generated by rotating the region enclosed by y = sin(x) and the x-axis, from x = 0 to x = π about the x-axis?

• π²

• π²/2

• 4π²

• π/2

If the region enclosed by y = 3x², y = 3 is revolved about the x-axis, what is the volume of the solid generated?

• 72π/5

• 27π/2

• 27π/20

• 9π/10

A right circular cone and some of its measurements are shown in the diagram below.
Based on the diagram, which of the following is closest to the volume of the cone?

• 13 cm³

• 38 cm³

• 113 cm³ 

• 151 cm³

Find the volume of the solid formed when you rotate the area in the first quadrant from the function y = x e^-x around the y axis.

• Diverges

• 4π

• π / 2

• π / 4

The volume of a cone is increasing at a rate of 6pi in^3/min. At time t=k, the radius of the cone is 2in, the height of the cone is 3in, and the height is increasing a a rate of 3/2 in/min. What is the rate at which the radius is increasing?

• 1

• 1 in/min

• 2

• 2in/min