SOLUTION: You plan to build a fish tank with three different types of materials. The bottom will be made of slate and cost $8 per square inch. The back wall will be opaque glass and will c

Question 657340: You plan to build a fish tank with three different types of materials. The bottom will be made of slate and cost $8 per square inch. The back wall will be opaque glass and will cost $5 per square inch. The front and two ends will be made of clear glass and will cost 0.70 per square inch. The ends of the tank will be square and the take will hold 10,000 cubic inches of water. Write an equation for the total cost of the materials needed to build the tank in terms of length L.
Answer by kevwill(135) (Show Source): You can put this solution on YOUR website!
Let's start with the formula for volume:

We are told the ends are square, so
and
We are also told that the volume is a constant 10,000 cubic inches, so we have

Solving for H:

The area of the bottom is:

The areas of the back and front are the same as the bottom:

And the total area of the two ends are:

The cost for the bottom is

The cost for the back is

The cost for the front is

And finally, the cost for the two ends is

So the total cost of the aquarium is

Combining terms:

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