Area of a Circle?

Question

Did I do this right?

What is the area of a circle with diameter 34mm?

R = 1/2 34 = 17
A = pi r^2
So 3.14 x 289

Area = 907.46 mm

Is this correct?

Answer 1

You are correct except it would be mm^2. (and assuming that you substitute 3.14 for pi.)

Techinically, 3.14 is an approximation of pi, since it is an irrational number (3.1415...).

The exact area would merely be 289pi mm^2.

Otherwise, your answer is fine.

Answer 2

Yes, with two caveats: The precision of your data is only two digits, so the accuracy of your answer can only be two digits even if the value of pi is given to hundreds of digits. If you use a more accurate value of pi, such as 3.141592654, the formula gives you 907.9 mm^2, not 907.46 mm^2. Rounding both of these to two digits gives you the same answer, however, namely 910 mm^2.

The other thing is that you forgot to square the mm since that's how areas are measured.

But anyone can use a formula - it's much more fun to see *why* pi is what it is. Archimedes did it with geometry way before calculus was invented. Here's the method: draw a circle and inscribe a regular polygon, then add up the areas of each polygon. The more sides the polygon has the more it looks like a circle and the closer the result will be to pi (if you use a radius equal to 1 to make it simpler).

The area of a regular polygon is found by drawing lines from the center to each vertex, forming equal isosceles triangles and using 1/2*base*height. The central angle of each triangle is given by 360/n degrees, and each of the other angles will be (180 - 360/n) / 2, where 'n' is the number of sides of the polygon.

Answer 3

Yes. Don't forget the units. It's mm squared.

Answer 4

17 squared time Pi. Yeah, that looks right to me.

Answer 5

yes, except the unit is no longer mm it is mm^2.

Otherwise, great job!

Answer 6

it's mm^2 but other than that yes

Answer 7

Spot on! Nice job!

:)

Answer 8

yea, but where are the units

Answer 9

yup..