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Presentation transcript:

The graph:

Similarly,

parisa yazdjerdi

Volume of Solids

Definition of Volume

Exercises (about the x-axis)

Find the volume v resulting from the revolution of the region bounded by: y=√x, from x=0 to x=1 about the x-axis.

Find the volume v resulting from the revolution of the region bounded by: y=√(a 2 -x 2 ) from x=-a to x=a and the x-axis about the x-axis.

Exercises (about the y-axis)

Find the volume of the solid of revolution generated by rotating the curve y = x 3 between y = 0 and y = 4 about the y-axis.

Nadine Bleibel A cylinder is a simple solid which is bounded by a plane region B1- which is called the base. A cylinder also has a congruent region B2 in a Parallel plane. The formula for volume for a circular cylinder is V=(Pi)r^2(h)

Nadine Bleibel Find the Volume of the solid obtained by rotating About the x-axis the region under the curve y= √x from 0 to 1.

Nadine Bleibel EXAMPLE: Find the volume of the solid obtaining by rotating about the y-axis the region bounded by y = x3, y = 8, and x = 0.