What is the volume of a rectangular prism that has a height of 10 1/2 in., a length of 6 2/3 in., and a width of 2 1/4 in.? Is it large enough to hold an item that has a height of 8 in., a length of 6 in., and a width of 2 in.?

Answer 1

To calculate the volume of the rectangular prism, we use the formula:

Volume = length x width x height

Plugging in the values:

Volume = (6 2/3) * (2 1/4) * (10 1/2)
Volume = 20/3 * 9/4 * 21/2
Volume = 630/12
Volume = 52.5 cubic inches

The volume of the rectangular prism is 52.5 cubic inches.

Now, let's compare the volume of the rectangular prism to the volume of the item with dimensions 8 in. x 6 in. x 2 in.

Volume of the item = 8 * 6 * 2 = 96 cubic inches

Since the volume of the item is 96 cubic inches, which is larger than the volume of the rectangular prism (52.5 cubic inches), the rectangular prism is not large enough to hold the item with dimensions 8 in. x 6 in. x 2 in.