Question
What is the volume of rectangular prism that has a high 13 and 1/2 in a length of 6 and 2/3 in and a width of 2 and 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
Answers
GPT 3.5
To find the volume of the 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 13 1/2
Convert the mixed numbers into improper fractions:
6 2/3 = 20/3
2 1/4 = 9/4
13 1/2 = 27/2
Now, multiply the fractions together:
Volume = (20/3) x (9/4) x (27/2)
Volume = 405/2 ≈ 202.5
The volume of the rectangular prism is 202.5 cubic inches.
Now, check if the item with dimensions 8 x 6 x 2 inches can fit inside the prism.
The volume of the item = 8 x 6 x 2 = 96 cubic inches
Since the volume of the item is smaller than the volume of the prism, the item can fit inside the prism.
Volume = length x width x height
Volume = 6 2/3 x 2 1/4 x 13 1/2
Convert the mixed numbers into improper fractions:
6 2/3 = 20/3
2 1/4 = 9/4
13 1/2 = 27/2
Now, multiply the fractions together:
Volume = (20/3) x (9/4) x (27/2)
Volume = 405/2 ≈ 202.5
The volume of the rectangular prism is 202.5 cubic inches.
Now, check if the item with dimensions 8 x 6 x 2 inches can fit inside the prism.
The volume of the item = 8 x 6 x 2 = 96 cubic inches
Since the volume of the item is smaller than the volume of the prism, the item can fit inside the prism.