Question

What is the volume of a rectangular prism that has a higher 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 night of 8 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 find the volume of a rectangular prism, you multiply the length, width, and height.

Given the dimensions of the first rectangular prism:
Height = 10 1/2 in = 21/2 in
Length = 6 2/3 in = 20/3 in
Width = 2 1/4 in = 9/4 in

Volume = Height x Length x Width
Volume = (21/2) x (20/3) x (9/4)
Volume = 315 cubic inches

Now, let's compare the volume of the first rectangular prism with the dimensions of the items:
1. Item with a height of 8 in, a length of 6 2/3 in, and a width of 2 1/4 in:
Volume = 8 x (20/3) x (9/4)
Volume = 480 cubic inches

Since 480 cubic inches is greater than 315 cubic inches, the first rectangular prism is large enough to hold this item.

2. Item with a height of 8 in, a length of 6 in, and a width of 2 in:
Volume = 8 x 6 x 2
Volume = 96 cubic inches

Since 96 cubic inches is smaller than 315 cubic inches, the first rectangular prism is also large enough to hold this item.