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For the following exercises, use the requested method to determine the volume of the solid.
439. The volume that has a base of the ellipse
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- Find the volume of the solid of revolution that results when a right triangle with legs of lengths 5 in. and 7in. is rotated about the 7in.leg. Use 227.arrow_forwardThe base of a right prism is a regular hexagon whose sides are 8cm in length. The height of the prism is 13 cm. Find the a Lateral area b total area c volume.arrow_forwardFind the volume of the described solid. 7) The solid lies between planes perpendicular to the x-axis at x = -5 and x = 5. The cross sections perpendicular to the x-axis are circular disks whose diameters run from the parabola y = x² to the parabola y = 50-x². Include a graph as part of your answer.arrow_forward
- Column A 1. Find the volume generated by revolving the first quadrant area bounded by the y² = 8x and its latus rectum (* = 2) about the x-axis. parabola 2. Find the volume generated by revolving the area bounded by the parabola y² = 8x and its latus rectum (x = 2) about the latus rectum. 3² 3. Find the volume generated by revolving the area bounded by the parabola about the y-axis. = 8x and its latus rectum (x = 2) 4. Find the volume generated by revolving the area cut off from the parabola y = 4x - x² by the x-axis about the line y = 6. 5. Find the volume of solid generated by revolving the region bounded by the x-axis and one arc of Y = sin about the x-axis. 6. Find the volume of solid generated by revolving bout the = 4x, x = 0, y = 4 about y = 4. a. 128 5 1408 b. 15 32 d. 3 T cubic units 256 e. 15 T cubic units cubic units π cubic units T cubic units f. 167 cubic units Column Barrow_forwardYou are eating Frosted Flakes, and you notice the box is a rectangular prism. The box is 12 inches tall, 8 inches long, and 3 inches wide. What is the lateral surface area of the box of Frosted Flakes?arrow_forwardThe fuel tank on a truck has trapezoidal cross sections with the dimensions (in feet) shown in the figure below. Assume that the engine is approximately 3 feet above the top of the fuel tank and that diesel fuel weighs approximately 53.1 pounds per cubic foot. Find the work done by the fuel pump in raising a full tank of the fuel to the level of the engine. y 4 3 2 1 14arrow_forward
- An artificial wetland has been created by building an earth dam across a small creek, between the sides of the creek valley. The dam is trapezoidal in section. It is 1.5 m across on the top and 1.53 m high. The sides are sloped at 1V:5H. The height of the dam is 1.53 m and the dam is 27.3 m long. What volume of earth is contained in the dam? Express your answer to the nearest integer value. If the average density of the earth in the dam is 2.28 tonnes/m3, how many tonnes of earth have been used to build the dam? Express your answer to the nearest integer value. Submit your work as a file in the accompanying question.arrow_forwardQ#5 A cuboid of length 12 cm and breath 9 cm has a total surface area of 426 ??2 .i- Find the height of the cuboid.ii- Find its volume.arrow_forwardUse the disk method to find the volume of revolution generated by revolving the region bounded by the graphs of the given equations about the indicated axis. y = 3√x ,the y-axis, y = 3; about the y-axisarrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,