A rectangular box, open at the top, has a volume of 256 cubic units. a) What must be the dimensions of this box, such that its total surface area is a minimum?

As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in. are cut from the corners of a rectangular piece of poster board that is 20 in. wide by 30 in. long. Kristine creates an open box by cutting congruent squares from the four corners of a square piece of cardboard that has a length of 24 in. per side. If the congruent squares that are removed have sides that measure 6 in. each, what is the volume of the box formed by folding and sealing the flaps?

For the right triangular prism found in Exercise 16, suppose that the sides of the triangular base measures 3 ft, 4 ft, and 5 ft. The altitude is 6 ft in length. a Find the lateral area of the prism. b Find the total area of the prism. c Find the volume area of the prism.

If the radius length of one sphere is three times as long as the radius length of another sphere, how do the surface areas of the spheres compare? How do the volume compare?

For the right triangular prism, suppose that the sides of the triangular base measure 4 m, 5 m, and 6 m. The altitude is 7 m. a Find the lateral area of the prism. b Find the total area of the prism. c Find the volume of the prism.

If the tank in Exercises 41 needs to be painted and 1 pint of paint covers 50ft2, how many pints are needed to paint the exterior of the storage tank? A cylindrical storage tank has a depth of 5 ft and a radius measuring 2 ft. If each cubic foot can hold 7.5 gallon of gasoline, what is the total storage capacity of the tank measured in gallons?

Given that a regular polyhedron of n faces is inscribed in a sphere of radius length 6 in., find the maximum largest possible volume for the polyhedron.

The 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.