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kiruha [24]
2 years ago
8

Find a formula for the described function. An open rectangular box with volume 3 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.
Mathematics
1 answer:
Alex73 [517]2 years ago
4 0

Answer:

SA(x) = x^2 + \frac{12}{x}

Step-by-step explanation:

Given

V = 3m^3 --- volume

x \to base\ length

y \to height

Required

The surface area as a function of base length

The volume (V) is calculated as:

V = Base\ Area * Height

V = x*x*y

V = x^2*y

Make y the subject

y = \frac{V}{x^2}

Substitute 3 for V

y = \frac{3}{x^2}

The surface area of the open box is:

SA = x^2 + 2xy+2xy

SA = x^2 + 4xy

Substitute: y = \frac{3}{x^2}

SA = x^2 + 4x*\frac{3}{x^2}

SA = x^2 + 4*\frac{3}{x}

SA = x^2 + \frac{12}{x}

Hence, the function is:

SA(x) = x^2 + \frac{12}{x}

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