Question

A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 686 cubic feet. The concrete for the base costs $8 per square foot, and the material for the roof.

Answer 1

To find the dimensions of the storage shed with a given volume, set up an equation and solve for the side length and height of the base. The cost of the base can also be calculated using the given cost per square foot.

Step-by-step explanation:

To find the dimensions of the storage shed, we need to solve for the length, width, and height of the box.

Let's assume that the length of the base is x, so the width of the base would also be x since it is a square base.

The volume of the box is given as 686 cubic feet, so we can set up the equation x^2 * h = 686, where h is the height of the box.

Now we have a quadratic equation to solve. We can rearrange the equation to get h = 686 / (x^2). You can plug in different values of x to find the corresponding value of h. Make sure to choose positive values for x and h since they represent physical dimensions.

The cost of the base is given as $8 per square foot. Since the base of the box is a square with side x, the cost of the base would be 8 * x^2.

Unfortunately, the question does not provide the cost of the material for the roof, so we can't calculate the total cost of the shed.