thanks!A cuboid has a volume of $\displaystyle 8 m^3$. The base of the cuboid is square with sides of length x metres. the sureface area of the cuboid is $\displaystyle A m^2$.Show that $\displaystyle A=2x^2+\frac{32}{x}$
thanks!A cuboid has a volume of $\displaystyle 8 m^3$. The base of the cuboid is square with sides of length x metres. the sureface area of the cuboid is $\displaystyle A m^2$.Show that $\displaystyle A=2x^2+\frac{32}{x}$
The side lengths are $\displaystyle x, x, y$.
The volume is
$\displaystyle V = x^2y$
So $\displaystyle 8 = x^2y$
$\displaystyle y = \frac{8}{x^2}$.
The surface area is
$\displaystyle TSA = 2x^2 + 4xy$
So $\displaystyle A = 2x^2 + 4xy$
$\displaystyle A = 2x^2 + 4x\left(\frac{8}{x^2}\right)$
$\displaystyle A = 2x^2 + \frac{32}{x}$.
Please you can leave the question out of quotation tags please? It makes it easier to follow when replying
What is known:
Use the formula for the volume of a cube, given that you have a square base an $\displaystyle x^2$ term should appear. It will be easiest to introduce a new variable for the height - $\displaystyle h$ in my case.Code:$\displaystyle V = 8m^3$ square base. $\displaystyle A_s = Am^2$
Spoiler:
You can now get an expression for the surface area given that it is equal to the sum of it's faces. If you draw a diagram you should be able to find the expression more easily.
Spoiler:
You have simultaneous equations to solve now. Eliminate h as it's not being asked for and get the expression for A