How many square feet in a 73 inch circle 10 inches deep?

Answer 1

Assuming you mean 73 inch diameter, the shape you are referring to sounds like a cylinder, and you are asking for the volume, in which case you would want cubic feet.

Remember any unit length squared would be an area. An area is a two-dimensional measurement. In its simplest terms, think of a square; you would multiply the length of two sides, and since they both have the same unit length, the unit becomes squared because units, like feet, or inches, or meters, are multiplied by themselves and called squared, so 2 feet multiplied by 2 feet would be 2 * 2 = 4, feet * feet = feet squared, so the most correct way to state this result would be 4 feet squared. As a unit of area, feet squared, and typically any squared unit length, is renamed to square feet for simplicity and just as a general convention.

Now, in this particular problem, you have added a thirddimension of length. The reason you may have thought there were only two is because circles are often referred to with one characteristic dimension. Think of it like a square: because the sides of a square all have the same length, you only need that one number to fully define the square in all aspects: let's say the square has one side length of 2 feet; it's perimeter length is 8 feet (4 * 2 feet), and its area is 4 square feet (2 feet * 2 feet). With a circle, you also only need one dimension: either its radius (the distance from the exact center of the circle to any point on its circumference), or its diameter (simply 2 * the radius, or the distance from of a straightline starting at one point on the circumference, going through the center, then ending at another point on the circumference). The reason we only need one dimension is because all other characteristics are relative to two numbers: the radius (or if you choose, the diameter), and a special constant number called Pi, which has no units; instead, Pi is a special number defined as the ratio of a circle's circumference to its diameter (or Pi = circumference / diameter); where a true square has four sides of equal length, a true circle has a "circumference-to-diameter ratio" equal to Pi. As a side note about Pi: Pi is what is known as an irrational number; by definition, Irrational Numbers cannot be represented in our number system (base 10, but we won't go into that here) by any fraction, or ratio of two integers (whole numbers without a decimal, like 1, 2, 3, 10, 99, 535, etc.), and therefore the have a decimal part that never ends (because if there is a limit to the number of digits in the decimal portion of the number, then there is a fraction that can represent that decimal); that being the case, and since Pi is defined as a ratio of circumference divided by diameter, at least one of those two numbers, either the circumference or the diameter must be irrational also. Usually, the diameter is a rational number, because it can be easily measured and defined, since it is a straight line, and so usually the length of the circumference is an irrational number, and can only be approximated (also, Pi can only be approximated as well). Here's Pi to 13 decimal places:

3.1415926535898...

In this discussion, we'll only need 2 decimal places for Pi, or 3.14; So, for example, say we have a circle with a 4 foot diameter; it's perimeter or circumference is 2 * Pi * radius, or Pi * diameter = 3.14 * 4 feet = 12.6 feet. Its area is Pi * radius-squared (Pi*r^2) or (Pi * diameter^2 ) / 4 = Pi * (2 feet * 2 feet) = 12.6 square feet; don't let the answers confuse you; because i used 2 feet for the radius, in one answer i used the diameter, which is 2 * the radius, and in another i used radius-squared; because the radius is 2, 2 * 2 = 2^2 = 4; though the circumference and the area have the same value, their units are very different and mean two very different things; it was purely coincidental that their values were the same. Try this excercise with a different radius, like 3, or 6, or 5 and you'll find that this won't be the case; but the principles are the same.

So, to finally answer the question, assuming you wanted the volume of a cylinder, which is a shape that has a circular cross-section, you need only the information i gave you to find the area of the circle, convert 73 inches to feet (73 inches * 1 foot / 12 inches = 73/12 feet = 6.08 feet), then simply multiply the area of the circle, which should now be in square feet, by the length of the cylinder (again convert inches to feet, or 10/12 feet = 0.83 feet): Pi * (6.08 feet / 2)^2 = 29.1 square feet * 0.83 feet = 24.22 feet^3 = 24.22 cubic feet; the volume of this cylinder.