What is the volume, in feet, of a rectangular prism with a height of 2 1/2 ft, a length of 2 1/4 ft, and a width of 3 1/8 feet? Your answer should be a mixed number and in simplest form.
To find the volume of a rectangular prism, you multiply the length, width, and height.
Volume = length x width x height
Volume = (2 1/4 ft) x (3 1/8 ft) x (2 1/2 ft)
First, convert all mixed numbers to improper fractions:
2 1/4 = 9/4
3 1/8 = 25/8
2 1/2 = 5/2
Now, multiply the fractions:
Volume = (9/4) x (25/8) x (5/2)
Volume = 225/64 ft^3
Next, change the improper fraction to a mixed number:
225 ÷ 64 = 3 with a remainder of 33
So, the volume of the rectangular prism is 3 33/64 ft.
No. In simplest form. Simplify the answer as much as possible.
Apologies for the oversight. Let's simplify the answer further.
The volume we calculated is 3 33/64 ft. To simplify this mixed number, we can convert it back into an improper fraction:
3 33/64 = (3 * 64 + 33) / 64
= 192 + 33 / 64
= 225 / 64
Therefore, the simplified volume of the rectangular prism is 225/64 ft.
Is there a way to keep the answer a mixed number and in the most simplest form possible?
Yes, we can express the fraction 225/64 as a mixed number in simplest form.
To convert the fraction 225/64 into a mixed number, divide 225 by 64:
225 ÷ 64 = 3 with a remainder of 33
Therefore, the mixed number in simplest form for the volume is 3 33/64 ft.