1) Using the graph, what is the value of x that will produce the maximum volume?
2) The volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 121 cubic centimeters.
Write h as a function

A large novel is divided into a three volume set. The pages of the novel are numbered consecutively, beginning with page 1 of volume 1 to the last page of volume 3 (in other words, if the last page of volume 1 is 324, then the first page of volume 2 is 325). There are an equal number of pages in each volume. If the sum of the nu

Finding formulas for the volume enclosed by a hypersphere in n-dimensional space.
c) Use a quadruple integral to find the hypervolume enclosed by the hypersphere x^2 + y^2 + z^2 + w^2 = r^2 in R^4. (Use only trigonometric substitution and the reduction formulas for ∫sin^n(x)*dx or ∫cos^n(x)*dx.)

If 2400 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
Volume = cubic centimeters.

Find the volume of the following region in space: The first octant region bounded by the coordinate planes and the surfaces y=1-x^2, z=1-x^2.
This question is #12 (section 9.3) in Advanced engineering mathmatics (8th ed.) by Kreyszig.
This section deals with the evaluation of double integrals.

A.) let A be the area of a circle of radius r that is changing w/ respect to time. if dr/dt is a constant, is dA/dt a constant, explain.
b.) let V be the volume of a sphere of radius r that is changing w/ respect to time. If dr/dt is constant, is dV/dt constant, explain.
c.) All edges of a cube are expanding at a rate of

Find the volume of the solid bounded by x = 0, y = 0, z = 0 and x + 2y + 3z = 6 by triple integration.
keywords: integration, integrates, integrals, integrating, double, triple, multiple