A cylindrical tube with ngligible thichness is placed into a rectangular box that is 3 inches by 4 inches by 8 inches, as shown in the accompanying diagram. If the tubes fits exactly into the box diagonally from the bottom left corner to the top right back corner, what is the best approximately of the number of inches in the length of the cube?

A box is constructed by cutting 3-inche square from the corner of a square sheet of cardboard, as shown in the accompanying diagram, and then folding the sides up. If the volume of the box is 75 inches, find the number of square inches in the area of the original sheet of cardboard?

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 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 rectangular box is to be made form a sheet of 24 inch length and 9 inch wideth cutting out indetical squares of side length x from the four corners and turning up the sides What is the value of x for width the vulume is maximum ?

For Question 19-20 use the figure above A lamp shade with a circular base is an example of a solid shape called a frustrum. In the figure above, the shaded region represents a frustrum of a right cone in which the portion of the original cone that lies 12 inches below its vertex has been cut off by slicing plane (not shown) parallel to the base. Q. If the height and slant height of the frustrum are 8 inches and 10 inches, respectively, what is the number of inches in the radius length, R, of the original cone?

A rectangular box is to be made form a sheet of 24 inch length and 9 inch wideth cutting out indetical squares of side length x from the four corners and turning up the sides What is the maximum volume of the box ?

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?