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Volumes on infinite intervals Find the volume of the described solid of revolution or state that it does not exist.
34. The region bounded by
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- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.arrow_forwardA 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=13R2H13rh2arrow_forwardA soda can is made from 40 square inches of aluminum. Let x denote the radius of the top of the can, and let h denote the height, both in inches. a. Express the total surface area S of the can, using x and h. Note: The total surface area is the area of the top plus the area of the bottom plus the area of the cylinder. b. Using the fact that the total area is 40 square inches, express h in terms of x. c. Express the volume V of the can in terms of x.arrow_forward
- f(x)= Let fbe the function defined by graph of fand the horizontal line Y=1, as shown in the image below. Region R -3 -2 (a) Find the area of R. 15 5+3x². Let R be the shaded region bounded by the -1 2 0 R 2 3 (b) The region Ris rotated around the x-axis. Find the volume of the resulting solid. (c) Let (x) be the vertical distance between the point (x, f(x)) and the horizontal line y=1, Find the rate of change of r(x) with respect to x at X=-1.arrow_forwardThe base of a three-dimensional figure is bound by the y-axis and the curve x = -3y2 + 6 on the interval [-1, 1]. Vertical cross sections that are perpendicular to the y-axis are right triangles with a height equal to 6. Find the numerical volume of the figure. 3-2 -1LA2 6 7 O V= 48 O V= 30 45 O V = 3 O V=arrow_forwardI = Suppose that R is the finite region bounded by f(x) = √ and f(x) 4 Find the exact value of the volume of the object we obtain when rotating R about the x-axis. V Find the exact value of the volume of the object we obtain when rotating R about the y-axis. V =arrow_forward
- The area formed by given functions and the y-axis is to be rotated about the y-axis by 180 degrees. Determine the volume of the solid formed.arrow_forward(Solid of Revolution about Horizontal Line (Washer)arrow_forwardK Find the volume of the solid generated by revolving the region bounded by the graphs of y = 2x² + 1 and y = 2x + 6 about the x-axis. ... The volume of the solid generated by revolving the region bounded by the graphs of y = 2x² + 1 and y = 2x + 6 about the x-axis is cubic units. (Round to the nearest hundredth.)arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
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