Question

How do I determine the area under this semicircle without using numerical approximation?

Answer 1

The area of a circle is A = pi * r^2
The radius is 3, and this is half of a circle
The area is then 3^2 * pi / 2 = (9/2) * pi

Answer 2

I think that might be considered numerical approximation.

Answer 3

Radius = 3, so the area would be like 1/2(pi * r^2) where your r = 3. Since it's a multiple of pi, it's an exact answer, otherwise you could just do an integral of it.

Answer 4

Take the integral of sqrt(9-x^2) = F(x)
The area is then F(3) - F(-3)

Answer 5

I think they don't want me to use integration on this.

Answer 6

I believe my first solution avoids numerical approximation, whereas the second does not...

Answer 7

I said semicircle because it looked like one. It's not stated that it is a semicircle, so I'm not sure it counts as one.

Answer 8

This is a semicircle... y = sqrt(9-x^2)
so y^2=9-x^2
x^2+y^2 = 9

The standard equation of a circle is
x^2 + y^2 = r^2

Answer 9

ohh....okay. Thanks!!