## Mathematics Construction

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 m2.

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 m2, 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 ±√( b2 -4ac))/2a

The part of the formula b2– 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.

#### Try these questions

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 rA = (pi)r2

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)r2 ) + 2(pi)rh

= 2( (pi) (32) ) + 2(pi) (3)(20)

= 2( (pi) × 9 ) + 120(pi

= 18(pi) + 120(pi

= 138(pi)

Therefore, 138(pi) square feet was used.