Question

Find a formula for the described function. An open rectangular box with volume 4 m3 has a square base. Express the surface area SA of the box as a function of the length of a side of the base, x. SA = m2 State the domain of SA. (Enter your answer in interval notation.)

Answer 1

Answer:

Surface area = $x^{2} +\frac{16}{x}$ m².

And domain will be x∈ (0,∞)

Step-by-step explanation:

An open rectangular box with volume 4 m³ has a square base.

The length of a side of the base is x

We can say that $x\times x\times h=4$

=> $x^{2} h=4$

$h=\frac{4}{x^{2} }$

Surface area can be found as: $x^{2} +4hx$

$x^{2} +(4x\times\frac{4}{x^{2}})$

Surface area = $x^{2} +\frac{16}{x}$ m².

And domain will be x∈ (0,∞) we can also say x>0

x is greater than zero as the surface area will always be a positive value and x cannot be negative.