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- SOLID OF REVOLUTION Find the volume of the solid of revolution of the section bounded by the line y=4x and the parabola y=x2 rotated with the x-axis as the access of the revolution. Solve using the disk and washer method. Solve again using the shell method.Applied Maximums and Maximums 7. (a) Determine the dimensions of the least expesive cylindrical can the will hold 100 cubic inches if the materials cost 2 cent , 5 cent and 3 cent, respectively, for the top, bottom ad sides. b. how do the dimensions of the least expensive can change if the bottom material cost more tha 5 cent per square inch?Solids of revolution Determine the volume generated about x-axis the area enclosed by 4x - y² = 4, x = 2 and x-axis Answer the following using those methods; a. using circular disk with graph b. using cylindrical shell with graph
- 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. Use both the method of disks and the method of shells. You will have two pictures, with a rectangle for each method. State the method used to find the volume each time. Write a brief statement comparing your answers. y= e^x, x= 0, y= pi, is rotated about the x - axis.Volume of a Rocket A rocket consists of a right circularcylinder of height 20 m surmounted by a cone whose heightand diameter are equal and whose radius is the same as thatof the cylindrical section. What should this radius be(rounded to two decimal places) if the total volume is to be500p/3 m3?Question: Find the volume formed by rotating about the y-axis the region enclosed by:x = 10y ; y3 = x ; y (greater than or equal to) 0 My Comments: How do you find the bounds and which method would you use? The question doesn't specify which method and I'm also confused on which function to use for the height and which variable to use for the radius for the cylindrical shell method. (Assuming that is the right method to use.)
- INTEGRAL CALCULUS* Show complete solution, please. 5. The first quadrant area bounded by 8x − y^2 = 0 and x = 2 is revolved about the x-axis. Solve for the volume of the solid of revolution generated.6. The first quadrant area bounded x^2 − 4x + y = 0 and the x-axis is revolved about 6 − y = 0. Solve for the volume of the solid of revolution generated.7. Solve for the volume generated when the plane area bounded by x^2 + 3x − 6 + y = 0 and 3 − y = 0 is revolved about 3 − x = 0.8. Solve for the volume generated when the plane area bounded by x^2 + 3x − 6 + y = 0 and 3 − y = 0 is revolved about the y-axis.Solids of Revolution:Cylindrical Shell Method Find the volume of the solid generated by revolving the area bounded by the given curves about the indicated axis. (show graph and complete solution)We want to construct a cylindrical container. We have 550 cm2 of metal. What dimensions would maximize the volume of the container? Enter exact values. radius of the base : r= cm height: h= cm
- Mass of a conical sheet A thin conical sheet is described by the surfacez = (x2 + y2)1/2, for 0 ≤ z ≤ 4. The density of the sheet in g/cm2 is ρ = ƒ(x, y, z) = (8 - z) (decreasing from 8 g/cm2 at the vertex to 4 g/cm2 at the top of the cone; see figure). What is the mass of the cone?Water sits in a hemispherical bowl of radius 7 cm. The depth of the water is 2 cm (i.e., from the surface of the water to the bottom of the bowl). Find the volume of water in the bowl.[Areas of Integration]Given the following graphs, find the volume of the solid of revolution of the shaded region.Rotate about the y-axis, using ring method and cylindrical shell method