Using the formula V=B×h , what is the volume of a rectangular prism with a width of 3 1/4 in., a length of 5 1/8 in., and a height of 7 3/8 in.? Your answer should be a mixed number in simplest form.(1 point) in^3
The volume of a rectangular prism is calculated by multiplying the base area (length x width) by the height.
In this case, the length is 5 1/8 in., the width is 3 1/4 in., and the height is 7 3/8 in.
First, calculate the area of the base:
5 1/8 in. x 3 1/4 in. =
41/8 in. x 13/4 in. =
((5 x 4) + 1)/8 in. x (3 x 4)/4 in. =
(20 + 1)/8 in. x 12/4 in. =
21/8 in. x 12/4 in. =
(21 x 12)/(8 x 4) in. =
252/32 in. =
7 7/32 in.
Then, multiply the base area by the height to get the volume:
7 7/32 in. x 7 3/8 in. =
223/32 in. x 59/8 in. =
(223 x 59)/(32 x 8) in. =
13177/256 in.
Therefore, the volume of the rectangular prism is 13177/256 cubic inches, which can also be expressed as 51 73/256 in^3 in simplest form.
not it
Apologies for the mistake in the previous calculation. Let's re-calculate the volume of the rectangular prism with the correct values.
Given:
Width = 3 1/4 in. = 13/4 in.
Length = 5 1/8 in. = 41/8 in.
Height = 7 3/8 in. = 59/8 in.
Using the formula V = B x h, where B is the base area (length x width):
Base area = (41/8) in x (13/4) in
Base area = (41 x 13) / (8 x 4) in^2
Base area = 533 / 32 in^2
Now, multiply the base area by the height:
Volume = (533/32) in^2 x (59/8) in
Volume = (533 x 59) / (32 x 8) in^3
Volume = 31447 / 256 in^3
Therefore, the volume of the rectangular prism with a width of 3 1/4 in., length of 5 1/8 in., and height of 7 3/8 in. is 31447/256 cubic inches in simplest form.