what is the area of a cirlcle with a diameter of 100mm?

Question

it gives me like these answers like:
50(pi)mm^2

2500(pi)mm^2

625(pi)mm^2

250(pi)mm^2 i just dont get it

Answer 1

area = pi times the radius squared

The diameter is twice the radius.

So divide the diameter in two, square that and multiply by pi.

Answer 2

Well, the area of a circle is A = (pi) * r^2, where r = the radius of a circle, and A = the area of the circle.

Now, you are given the diameter of a circle, which is 100 mm. Remember that the diameter of any circle is ALWAYS twice the radius, so to get the radius, use the equation dia = 2 * r, where dia = the diameter of a circle, and r is its radius. Rearrange the equation to solve for r, which gives you the equation r = dia / 2, so r = (100 mm) / 2, which gives you r = 50 mm.

Now you can just plug in your values and solve the equation for the area of the circle. You have A = (pi) x r^2, which in your problem would be A = (pi) x (50 mm)^2. Now square 50mm, which makes your equation look like this: A = (pi) * 2500 mm^2.

You might be getting confused by the units. When you multiply units against themselves, like you do when you square the length of a line, the units are raised to the power of the number of times they are multiplied. For example, length * length yields length raised to the power of two (length^2), which defines an area, and length * length * length yields length raised to the power of three (length^3), which defines a volume. But when you multiply plain old numbers together (these are known as scalars, you don't combine units with them), you treat them just like you always have done with numbers.

Therefore, correctly, you can write your answer to your problem as A = (pi)2500 mm^2 OR you and write it as 2500(pi) mm^2 OR even just 2500pi mm^2. Why, you may ask? Because the symbol pi is considered a shorthand of a number. I could use a very rough approximation of 3.14 for pi, and go ahead and multiply it out. If if I do that, I can't write pi in my answer, because I'll be squaring pi, which is not what the equation of the area of a circle wants you to do.

So, using 3.14 as the value of pi, the answer becomes A is about (the phrase 'is about' has to be used because pi is one of those numbers that just doesn't end, there are an endless parade of numbers trailing the .14 part, but that's another story) 7850 mm^2.

Now back to your list of numbers you gave, it looks like it's a multiple choice question, and it is wanting you to pick the right answer. The right answer should be 2500(pi)mm^2, which is the second choice.

Answer 3

Area = pi times Radius square

If your diameter is 100mm you radius is 50mm
Square 50 and you get 2500

So substitute that and you get
2500(pi)mm squared(^2)

Answer 4

A=(pi)r^2, that is, area equals pi times the square of the radius of the circle. Radius is 1/2 of the diameter. Because you are squaring the radius, the solution is in squared millimeters.

Answer 5

Area of circle= (pi) r^2 , where r is radius of circle.
radius(r) = diameter(d)/2
= 100 mm/2
= 50 mm
so area of circle= (pi). (50mm)^2
= (pi) . 2500 mm^2
= 2500. (pi) mm^2
so second choice is right answer.

Answer 6

hi, area of a circle = pi x radius2

the diameter is 100mm, thus the radius is 50mm

thus area = pi x 50mm2
= pi x 2500 mm2
=3,14 x 2500mm2
=7850mm2 (more or less)

Answer 7

area of a circle is pi r^2, where pi is pi, r is radius and ^2 is squared, since 2r = d, r = 50mm, therefore the first is correct.

Answer 8

The answe is 2500 (pi) mm^2
because your r = 50 mm

and area is pi x r^2

which is pi x (50 mm)^2

which is pi x (50)^2 x (mm)^2

which is pi x 2500 x mm^2

or for short 2500(pi)mm^2

Answer 9

A = ((d^2)/4)pi

A = ((100^2)/4)pi
A = (10000/4)pi
A = 2500pimm^2

The second answer is correct.