An open box with a square base is required to have a volume of 10 cubic feet. What is the surface area as a function of x?

Solution:

As per the condition given,

V = x²h

It is given that

Volume = 10 cubic feet

So substituting it

10 = x²h

10/x² = h

We know that surface area can be found using the formula

A = x² + 4(xh)

Substituting the value of h

A = x² + 4(x(10/x²))

By further simplification

A = x² + 4(10/x)

A = x² + 40/x

Therefore, the surface area as a function of x is A = x² + 40/x.

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An open box with a square base is required to have a volume of 10 cubic feet. What is the surface area as a function of x?

Summary:

An open box with a square base is required to have a volume of 10 cubic feet. The surface area as a function of x is A = x² + 40/x.