Sophie has a hard rubber ball whose circumference measures 13 inches. She wants to store it in a box. What is the number of cubic inches in the volume of the smallest cube shaped box with integer dimensions that she can use?

A 3-inch-tall rectangular box with a square base is constructed to hold a circular pie that has a diameter of 8 inches. Both are shown below. What is the volume, in cubic inches, of the smallest such box that can hold this pie?

The volume of a rectangle box is 144 cubic inches. The height of the solid is 8 inches. Which measurements, in inches, could be the dimensions of the base?

In the figure above, a rectangular container with the dimensions 10 inches by 15 inches by 20 inches is to be filled with water, using a cylindrical cup whose radius is 2 inches and whose height is 5 inches. What is the maximum number of full cups of water that can be placed into the container without the water overflowing the container?

What is the maximum number of boxes with dimensions 2 inches by 3 inches by 4 inches that could fit in a cube-shaped container that has a volume of 1 cubic foot?

A sealed cylindrical can holds three tennis balls each with diameter of 2.5 inches. If the can is designed to have the smallest possible volume, find the number of cubic inches of unoccopied space inside the can correct to the nearest tenth of a cubic inch.

Find the number of cuboidal boxes measuring 2cm by 3cm by 10cm which can be stored in a carton whose dimensions are 40cm, 36cm and 24cm.

A rectangular box with length 22 inches , width 5 inches , and height 5 inches is to be packed with steel balls of radius 2 inches in such a way that the centers of the balls are collinear. What is the maximum number of balls that can fit into the box, provided that no balls should protrude from the box ?

Jack has a box in the shape of the cube, the inside edges of which are 4 inches long. What is the longest object he could fit inside the box (i.e., What is the diagonal of the cube) ?

A square piece of cardbroad measuring x inches by x inches is to be used to form an open box by cutting off 2-inch squares, and then folding the slides up along the dotted lines, as shown in the figure above. If x is an integer , and the volume of the box must be greater than 128 cubic inches , what is the smallest value of x that can be used ?