# Thread: Express the area as a function

1. ## Express the area as a function

A rectangle has perimeter 20m. Express the area of the rectangle as a function of the length of one of its sides.

$A(L) = ??$

Thanks for the help.

2. The perimeter of the rectangle is $2l + 2w = 20$

so $w = 10 - l$.

The area of the rectangle is $A = lw$

$A = l(10 - l)$

$A = 10l - l^2$.

3. 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. $v = a * h$

Step 2. surface area of cube = $6a^2$

Step 3. answer: $a = v/h$

Step 4. surface area of cube = $6(v/h)^2$

$A(v) = 6(v/h)^2$

Am I correct?

4. Hello, hydride!

Express the surface area of the a cube as a function of the its volume.

Let $s$ = side of the cube.

Then its volume is: . $V \:=\:s^3 \quad\Rightarrow\quad s \:=\:\sqrt[3]{V}$

The surface area is six times the area of a face: . $A \:=\:6s^2$

Therefore: . $A \;=\;6\left(\sqrt[3]{V}\right)^2 \;=\;6V^{\frac{2}{3}}$

5. Thanks!
I was close, but I understand now.