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.?(1 point)

Answer 1

To find the volume of the rectangular prism, you multiply the height, length, and width together:

Volume = height x length x width
Volume = 10 1/2 in. x 6 2/3 in. x 2 1/4 in.
Volume = (21/2) x (20/3) x (9/4)
Volume = (7/1) x (20/3) x (9/4)
Volume = 7 x 20 x 9 / 3 x 4
Volume = 1260 / 12
Volume = 105 cubic inches

The volume of the rectangular prism is 105 cubic inches.

Now we need to find the volume of the item to see if it will fit into the prism:

Volume of the item = height x length x width
Volume of the item = 8 in. x 6 in. x 2 in.
Volume of the item = 96 cubic inches

Since the volume of the item is 96 cubic inches, it is small enough to fit into the prism which has a volume of 105 cubic inches.