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 the height of 8 in a length of 6in and a width of 2 in?
To find the volume of a rectangular prism, you can use the formula:
Volume = length x width x height
Given the dimensions of the first rectangular prism:
Length = 6 2/3 inches = 20/3 inches
Width = 2 1/4 inches = 9/4 inches
Height = 10 1/2 inches = 21/2 inches
Volume = (20/3) x (9/4) x (21/2)
Volume = 315/3 = 105 inches
Therefore, the volume of the rectangular prism is 105 cubic inches.
Now, let's determine if the item with dimensions 8 x 6 x 2 inches can fit in the rectangular prism.
The volume of the item is:
Volume = 8 x 6 x 2 = 96 cubic inches
Since the volume of the item is less than the volume of the rectangular prism, the item can fit inside the prism.
wrong
Apologies for the mistake in the previous calculation. Let's correct the calculation.
Given the dimensions of the first rectangular prism:
Length = 6 2/3 inches = 20/3 inches
Width = 2 1/4 inches = 9/4 inches
Height = 10 1/2 inches = 21/2 inches
Volume = (20/3) x (9/4) x (21/2)
Volume = 105 cubic inches
The volume of the first rectangular prism is indeed 105 cubic inches.
Now, let's determine if the item with dimensions 8 x 6 x 2 inches can fit in the rectangular prism.
The volume of the item is:
Volume = 8 x 6 x 2 = 96 cubic inches
Since the volume of the item (96 cubic inches) is smaller than the volume of the rectangular prism (105 cubic inches), the item can fit inside the prism. Apologies for the confusion in the initial response. Thank you for pointing out the mistake.