SOLUTION: what dimensions would a rectangular prism have if its surface area was 160 fee square. Based on the answer what would the figure's volume be.
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Question 968969: what dimensions would a rectangular prism have if its surface area was 160 fee square. Based on the answer what would the figure's volume be.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Let , , and be the dimensions (in feet) of the rectangular prism.
Let's say .
The surface area of the base of that {box) is square feet.
The surface area of the top of that {box) is square feet.
The surface area of the sides of that {box) is square feet.
The total surface area of the base of that {box) in square feet is
is .
We are told that the total surface area is square feet, so we know that
<---><---> .
We can give values to and and solve for .
Then we can calculate the volume of that box (in cubic feet) as
, by multiplying together , , and .
Let's say that .
Then, substituting those values, we get
-->-->-->-->-->--> .
.
Let's say that .
Then, substituting those values, we get
-->-->-->-->--> .
.
Let's say that .
Then, substituting those values, we get
-->-->-->-->--> .
.
If we start with , we find
.
If we start with , we find
.
If we start with , we find
.
Other choices yield measurements that are not whole numbers.
For example, if we start with , we find
,
and if we wanted a cube, with , we would have
--->--->--->--->--->
and
NOTE:
The way to answer the question depends on the math level of the class where this question was asked.
Was it asked in elementary school? In a college advanced calculus class? somewhere in between.
I do not believe this is a question from a multivariate calculus class, but intuition would tell us that the rectangular prism with greatest volume will be a cube.
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