Algebra HW?

Question

The length of a diameter of the circle is 8. If there is a right angle and 1/4 of the circle is shaded. What is the shaded region?

a. 8 + 2 pi
b. 8 + 4 pi
c. 16 + 2 pi
d. 16 + 4 pi

IT HAS TO BE ONE OF THE ANSWERS ABOVE!!!!!!!!

Answer 1

area of circle = pi * r^2
radius = diameter/2

area of circle with diameter 8 :
pi * (8/2)^2
= pi * 4^2
= 16pi

one quarter of circle's area:
16pi/4
= 4 pi

don't see how any of the choices can be right, given your info.

Answer 2

You are leaving out some details. It cannot be one of the answers above considering the given information. What is the other information?

If the shaded region is the desired area, then you are looking at a ratio problem. Determine the area of the circle and divide by 4. The area is determined by pi * ((diameter) squared) / 4. Since you are dividing by four to get one fourth of the total area, the equation would be modified thusly:
pi * 8*8/(4*4)

Do the math. You could use a calculator or you could simply understand a little about multiplication. What you really have is pi * (2*2*(4*4))/(4*4)
This reduces to pi * 4

hope this helps. No calculator used.

Suppose the circumference were 8. Then 8 = pi * D
or D = 8 / pi. Then the area of the shaded region is pi*((8*8)/(pi*pi))/(4*4)
Canceling we get: (2*2*4*4/pi)/(4*4) This reduces further to 4 / pi.

Answer 3

Area is (pi)r^2.
So, if the radius is half the diameter, the radius is half of 8, or 4.
Then, (pi)4^2 is (pi)16.
But your question is to find 1/4 of the circle, not the whole circle, so 1/4 of 16(pi) is 4(pi). That's how the other helpers got their answers.
Always gotta show the work, right?

Answer 4

find the area and divide by 4.. or multiply by 0.25

Answer 5

4 pi. or 12.56