We want to construct a box with a square base and we currently only have 10m2 of material to use in construction of the box. Assuming that all material is used in the construction process, determine the maximum volume that the box can have.

The maximum volume of the box is:

Step-by-step explanation:

Given

Required

The maximum volume of the box

Let

The surface area of the box is:

So, we have:

Divide both sides by 2

Make b the subject

The volume of the box is:

Substitute:

Spit

Differentiate V with respect to a

Set to calculate a

Collect like terms

Multiply both sides by 2

Solve for a

Recall that:

Apply law of indices

So:

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.