A toy company packages modeling clay in the shape of a rectangular
prism with dimensions 6 inches by 1 inch by 1
2 inch. They want to change the shape to a
rectangular pyramid that uses the same amount of clay. Determine 2 sets of possible
dimensions for the pyramid.
Set 1:
Let the base dimensions of the rectangular pyramid be x inches by y inches. The height of the pyramid will be h inches.
Since the volume of the rectangular prism is the same as the volume of the rectangular pyramid:
6 * 1 * 12 = x * y * (1/3) * h
72 = (1/3) * x * y * h
216 = x * y * h
One possible set of dimensions for the pyramid could be:
x = 6 inches, y = 6 inches, h = 6 inches
Another possible set of dimensions for the pyramid could be:
x = 9 inches, y = 8 inches, h = 3 inches
Set 2:
Let the base dimensions of the rectangular pyramid be x inches by y inches. The height of the pyramid will be h inches.
Since the volume of the rectangular prism is the same as the volume of the rectangular pyramid:
6 * 1 * 12 = x * y * (1/3) * h
72 = (1/3) * x * y * h
216 = x * y * h
One possible set of dimensions for the pyramid could be:
x = 12 inches, y = 6 inches, h = 3 inches
Another possible set of dimensions for the pyramid could be:
x = 18 inches, y = 4 inches, h = 4.5 inches.