What is the volume, in cubic 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 ft.? Your answer should be a mixed number in simplest form.(1 point)
ft.(the power of 3)
The volume of a rectangular prism is calculated by multiplying 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 the 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 = (9 x 25 x 5) / (4 x 8 x 2)
Volume = 1125 / 64
Since the question asks for the answer in simplest form, we need to convert the improper fraction back to a mixed number:
1125 ÷ 64 = 17 with a remainder of 17
The volume is 17 17/64 cubic feet.
17 17/64 is wrong
Apologies for the mistake. Let's correct that.
To find the volume of the rectangular prism:
Volume = length x width x height
Volume = (2 1/4) ft x (3 1/8) ft x (2 1/2) ft
First, convert all the 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 = (9 x 25 x 5) / (4 x 8 x 2)
Volume = 1125 / 64
Now, let's simplify the fraction:
1125 ÷ 64 = 17 with a remainder of 37
Therefore, the volume of the rectangular prism is 17 37/64 cubic feet.