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- Maximum Volume A rectangular solid with a square base has a surface area of 337.5 square centimeters. (a) Determine the dimensions that yield the maximum volume.(b) Find the maximum volume.Cylinder in a cone A right circular cylinder is placed inside acone of radius R and height H so that the base of the cylinder lieson the base of the cone.a. Find the dimensions of the cylinder with maximum volume.Specifically, show that the volume of the maximum-volumecylinder is 4/9 the volume of the cone.b. Find the dimensions of the cylinder with maximum lateral sur-face area (area of the curved surface).Dimensión of box maximum volume are The maximum volume is
- rectangular box is inscribed in the region in the first octant bounded above by the plane with x-intercept 6, y-intercept,6 and z-intercept 6. Find dimensions of box of maximum volumepyramid 3 m high has a square base that is 3 m on a side. The crosssection of the pyramid perpendicular to the altitude x meters down from the vertex is a square x meters on a side. Find the volume of the pyramid.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.
- Volume of Solid of a Revolution Show full solution and graph. Thanks!A rectangle has one side on the x-axis and two corners on the top half of the circle of radius 1 centered at the origin. What is the maximum area of such a rectangle? What are the coordinates of the top-right vertex? x-coordinate _____ y-coordinate _____Derivation of a formula of volume cone (using Calculus, in two different ways).