If 1700 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

Step-by-step explanation:

Given

Required

Determine the largest possible volume

Represent the dimension with:

Surface Area with an open top is:

Substitute 1700 for Surface Area

Make h the subject

The volume (V) is calculated as:

Substitute value for h in

Differentiate and equate to 0, afterwards

Solve for

Take the square root of both sides

Substitute 23.80 for x in

So, the largest possible volume is:

square pyramid

step-by-step explanation:

square prism looks like nothing like that

triangular prism has a rectangular base instead of a square base

tetrahedron has a triangular base