Solve the problem.
-A closed box with a square base has to have a volume of 16,000 cubic inches. Find a function for the surface area of the box.
A) $S ( x ) = x ^ { 2 } + \frac { 64,000 } { x }$
B) $S ( x ) = 2 x ^ { 2 } + \frac { 64,000 } { x }$
C) $S ( x ) = 2 x ^ { 2 } + \frac { 16,000 } { x }$
D) $S ( x ) = 2 x ^ { 2 } + \frac { 96,000 } { x }$

Question

Quizplus · Accepted Answer

The volume of the box is given by $V = x^2h = 16,000$, where $x$ is the side length of the square base and $h$ is the height. To find the surface area $S(x)$, we need to consider the area of the base ($x^2$), the top ($x^2$), and the four sides ($4xh$). Since $V = x^2h$, we can solve for $h = \frac{16,000}{x^2}$. The surface area formula becomes $S(x) = 2x^2 + 4xh = 2x^2 + 4x(\frac{16,000}{x^2}) = 2x^2 + \frac{64,000}{x}$, which matches option B.

Solve the Problem S(x)=x2+64,000xS ( x ) = x ^ { 2 } + \frac { 64,000 } { x }S(x)=x2+x64,000​

Solve the Problem $S ( x ) = x ^ { 2 } + \frac { 64,000 } { x }$