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.?
A. 15 in.3 and no, the item will not fit inside the prism.
B. 157 1/2 in.3 and yes, the item should fit inside the prism.
C. 160 in.3 and yes, the item should fit inside the prism.
D. 3,780/24 in.3 and no, the item will not fit inside the prism
To find the volume of the rectangular prism, we use the formula: Volume = length x width x height
Plugging in the values given:
Volume = (6 2/3) x (2 1/4) x (10 1/2)
Volume = (20/3) x (9/4) x (21/2)
Volume = 30 x 9 x 21
Volume = 5670 in.3
Therefore, the volume of the rectangular prism is 5670 in.3.
Comparing this with the dimensions of the item:
Volume = 8 x 6 x 2
Volume = 96 in.3
Since 5670 in.3 is much larger than 96 in.3, the item should fit inside the prism. So the correct answer is option B: 157 1/2 in.3 and yes, the item should fit inside the prism.