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- A frustum of a cone is the portion of the cone bounded between the circular base and a plane parallel to the base. With dimensions are indicated, show that the volume of the frustum of the cone is V=13R2H13rh2Find the volume of the solid generated by revolving the region bounded by the graphs of the following equations about the indicated lines. Draw a picture of the region to be rotated along with a representative rectangle. state the method used to find the volume. xy=6, y=2, y=6, x=6, about the line x=6Find the volume of the solid generated by revolving the region bounded by the graphs of the equationsabout the x-axis. Express the result as an exact value. y=9-x2 , y=x+3
- Using the cylinder method determine the volume of the solid obtained by rotating the region bounded by x =y2-4 and x = 6-3y about the line y = -8.Find the volume of the solid generated by revolving the region bounded by the graphs of the following equations about the indicated line. Draw a picture of the region to be rotated along with a representative rectangle. Clearly indicate the METHOD that you are using. Give a brief explanation of why you chose to use that particular method. Then, find the volume. y= x^2, y= 2x, about the line x= -2.Using cylindrical shells find the volume of the solid obtained by rotating the region bound by y=x-x^2 and y=0 about the line x=2.
- Find the volume of the solid obtained by rotating the region bounded by y= x^2 —4x +5 , x=1, x=4 and the X-axis about the X-axis. A) get a sketch of the bounding region B) find the cross sectional area C) determine the limits of integration D) calculate the volume of the solidLook for the volume of the solid produced by rotating the region enclosed by y = sin x, x = 0, y =1 and about y =1 (Cylindrical) *Show the graph. Show your solution about the intersection points and the axis of revolution symbol and the stripSolid of revolution Find the volume of the solid generated when the region bounded by y = cos x and the x-axis on the interval [0, π/2] is revolved about the y-axis.
- Using the methods of shells find the volume of revolution formed by revolving around the x-axis the region bounded by y=x^1/3, y=0, and x=1Gabriel's horn is an infinite solid that is formed by taking the region enclosed by the curves y = 1/ (x3/4), x = 1, and the x-axis. Find the volume of the solid obtained by rotating the region about the x axis. (Or state that it's divergent).Region R in xy-plane is bounded by the curve y = 9sin(x) and the x-axis, between the lines x = 0 and x = pi. A solid is formed by revolving R around the y-axis. How to calculate the exact volume?