Solve.
-An open-top rectangular box has a square base and it will hold 103 cubic centimeters (cc). Each side of the base has length $x \mathrm {~cm}$, and the box has a height of $y \mathrm {~cm}$. Express the surface area $S$ as a function of the length $x$ of a side of the base.
A) $S ( x ) = \frac { 412 } { x } + x ^ { 2 }$
B) $S ( x ) = \frac { 206 } { x } + x ^ { 2 }$
C) $S ( x ) = 412 + x ^ { 2 }$
D) $S ( x ) = \frac { 103 } { x } + x ^ { 2 }$

Question

Quizplus · Accepted Answer

The volume of the box is given by $V = x^2y = 103$, so $y = \frac{103}{x^2}$. The surface area $S$ includes the base ($x^2$) and four sides. Each side has an area of $xy$, so the total area of the sides is $4xy = 4x\left(\frac{103}{x^2}\right) = \frac{412}{x}$. Therefore, $S(x) = x^2 + \frac{412}{x}$.

Solve -An Open-Top Rectangular Box Has a Square Base and It

Solve
-An Open-Top Rectangular Box Has a Square Base and It