Mathematics is constantly used in construction.

Consider your own room. If you want to put a new carpet in your room, and you know that your room is 4m long and 3 meters wide, calculate the number of square meters of carpet you will need.

Let l = length, w = width then the area = l w = 4(3) = 12 m^{2}.

The store has a roll of carpet 4 meters wide with 2 meters left on the roll. Is that enough for your room?

The square footage on the roll = f(x) = 4x where x = number of meters left on the roll.

f(x) = 4(2) = 8. Since you needed 12 m^{2}, this remnant is not large enough for your room.

More complicated construction involves drawing quadratic equations in order to cut out the parts. In a simple example of this you may be given a quadratic equation for the wing of a model airplane. There is a simple way to determine whether the parabola will cross the x-axis and how often. Using this will make drawing your part easier.

Remember the quadratic formula: x = (-b ±√( b^{2} -4ac))/2a

The part of the formula b^{2}– 4ac is called the discriminant.

If the discriminant is

- Negative, then the graph does not cross the x-axis.
- Zero, then the graph is tangent to the x-axis, i.e. touches it at one point.
- Positive, then the graph crosses the x-axis at two points, the solutions to the equation.

1. A water tank in the shape of a right circular cylinder is 20 ft long and 6 ft in diameter. How much sheet metal was used in its construction?

If the diameter is 6 ft, then the radius is 3 ft. The surface area of each end is given by the area formula for a circle with radius *r*: *A* = (*pi*)*r*^{2}.

The surface area of the cylinder is the circumference of the circle, multiplied by the height: *A* = 2(*pi*)*rh*.

Then the total surface area of this tank is given by:

2 ×( (*pi*)*r*^{2} ) + 2(*pi*)*rh*

= 2( (*pi*) (3^{2}) ) + 2(*pi*) (3)(20)

= 2( (*pi*) × 9 ) + 120(*pi*)

= 18(*pi*) + 120(*pi*)

= 138(*pi*)

Therefore, 138(*pi*) square feet was used.

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