A rectangle has perimeter 20m. Express the area of the rectangle as a function of the length of one of its sides.
$\displaystyle A(L) = ??$
Thanks for the help.
Thank you so much, I understand that one now. But now I am again stuck on one more questions.
Express the surface area of the a cube as a function of the its volume.
Step 1. $\displaystyle v = a * h$
Step 2. surface area of cube = $\displaystyle 6a^2$
Step 3. answer: $\displaystyle a = v/h$
Step 4. surface area of cube = $\displaystyle 6(v/h)^2$
$\displaystyle A(v) = 6(v/h)^2$
Am I correct?
Hello, hydride!
Express the surface area of the a cube as a function of the its volume.
Let $\displaystyle s$ = side of the cube.
Then its volume is: .$\displaystyle V \:=\:s^3 \quad\Rightarrow\quad s \:=\:\sqrt[3]{V}$
The surface area is six times the area of a face: .$\displaystyle A \:=\:6s^2$
Therefore: .$\displaystyle A \;=\;6\left(\sqrt[3]{V}\right)^2 \;=\;6V^{\frac{2}{3}}$