Express the plane \(z=x\) in (a) cylindrical, and (b) spherical coordinates.

Find the length of a diagonal of a \(4 m \times 12 m\) rectangle.

The volume of a cube is increasing at the rate of \(1200\ cm\ \frac{sup}{min}\) at the instant its edges are 20 cm long. At what rate are the edges changing at that instant?

Points B and D are points of tangency. Find the value of x.

.

A packing company is doing an inventory of boxes. Their most popular box is display below. You can use the formula \(V = lwh\) to find the volume of the box. The volume of the box is \(40 ft^{3}\). What is the value of x? Find the length and the width of the box. Describe any extraneous solutions.

The volume of a sphere is \(5,572.45 \in^3\) To the nearest inch, what is the radius of the sphere?