Perimeter and Area

Question

Luis made a round oak table that he wants to cover with glass. How many square feet of glass are needed if the distance across the center of the table is 4 feet?

Answer 1

Really, this question has nothing to do with the perimeter of the table, but DOES have to do with its area.

The second sentence tells us that the "distance across the center of the table is 4 feet"; this distance is the diameter of the table (and is the definition of the diameter of a circle).

The second sentence also asks "How many square feet of glass are needed"? Square feet is a measure of area, so the question really boils down to this: What is the area of the round table, which has a diameter of 4 feet?

The area of a circle is given by the equation A = pi * r^2 = pi * (d / 2)^2, where r = d / 2, and

A = area of the circle

pi = 3.1415926... (approximately)

r = radius of the circle

d = diameter of the circle

So, substituting numerical values into the variables, we get

A = (3.1415926) * (4 ft / 2)^2 = (3.1415926) * (2 ft)^2 = (3.141592653) * 4 sq ft, or

A = 12.57 sq ft (rounded to the nearest hundredth)

NOTEWORTHY, but only if useful: The value of pi is an irrational number, which means never-ending, non-repeating decimal; or more simply, it cannot be represented by a ratio. It CAN, however, be APPROXIMATED by a ratio. The ancient Babylonians used the ratio 355/113, which approximates pi to about 7 decimal places. So, if your answer needs only a few decimal places beyond the decimal point, this ratio might be useful to you.