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 the rectangular prism, you multiply the height, length, and width together:
Volume = 10 1/2 in. * 6 2/3 in. * 2 1/4 in.
Volume = 21/2 * 20/3 * 9/4
Volume = 315/2 * 20/3
Volume = 3150/6
Volume = 525 in. 3
Since the volume of the rectangular prism is 525 in. 3, it is large enough to hold an item with dimensions of 8 in. x 6 in. x 2 in. which has a volume of 8 * 6 * 2 = 96 in. 3. Therefore, the item should fit inside the prism.
So, the correct response is: 157 1/2 in. 3 and yes, the item should fit inside the prism.
can u try again
Apologies for the miscalculation. Let's calculate the volume correctly:
Volume = height * length * width
Volume = 10 1/2 in. * 6 2/3 in. * 2 1/4 in.
Volume = 21/2 * 20/3 * 9/4
Volume = 315/6
Volume = 52 1/2 in. 3
The correct volume of the rectangular prism is 52 1/2 cubic inches.
Now, let's check if the item with dimensions of 8 in. (height) x 6 in. (length) x 2 in. (width) will fit inside the prism. Calculate the volume of the item:
Volume = 8 in. * 6 in. * 2 in.
Volume = 96 in. 3
Since the volume of the item (96 in. 3) is greater than the volume of the prism (52 1/2 in. 3), the item will not fit inside the prism.
Therefore, the correct response is: 52 1/2 in. 3 and no, the item will not fit inside the prism.
pick the correct answer
The correct response is:
3,780/24 in. 3 and no, the item will not fit inside the prism.