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.?
Responses
157 1/2 in. 3 and yes, the item should fit inside the prism.
3,780/24 in. 3 and no, the item will not fit inside the prism.
160 in. 3 and yes, the item should fit inside the prism.
15 in. 3 and no, the item will not fit inside the prism.
To find the volume of a rectangular prism, you multiply the length, width, and height together.
Volume = length x width x height
Volume = (6 2/3) x (2 1/4) x (10 1/2)
Volume = (20/3) x (9/4) x (21/2)
Volume = (180/12) x (189/6)
Volume = (15) x (189)
Volume = 2835 in^3
The volume of the rectangular prism is 2835 cubic inches.
Since the item has a volume of 8 x 6 x 2 = 96 cubic inches, it should fit inside the prism since the prism has a larger volume of 2835 cubic inches.
Therefore, the correct response is: 160 in^3 and yes, the item should fit inside the prism.