Question

Find the area of the shaded region. Give your answers exactly (in terms of π) and rounded to the nearest hundredth.


a.

1,600 – 400π = 296.46 un2

c.

1,800 – 600π = 329.68 un2


b.

1,000 – 250π = 189.87 un2

d.

1,200 – 300π = 257.52 un

Answer 1

http://media.education2020.com/evresources/647-07-03-00-00_files/i0370000.jpg

Answer 2

Okay, well, first we find the area of the whole rectangle. How, though?

If the whole bottom is 60, and there are 3 circles connected to each other, then divide the bottom of the rectangle by 3. This will give you the diameter of each circle, which is 20. Because we know the diameter, we also know the height of the rectangle. Try rotating the diameter of any one of these circles from a horizontal position to a vertical position. You can see then that the diameter is indeed equal to the unknown side of the rectangle. Therefore, the area of the rectangle is 60 times 20, or 1200. Almost done. We're looking for the shaded region, so now we find the combined area of the circles. If the diameter of any one of these circles is 20, then the radius must be 10. The formula for finding the area of a circle is Pi*radius squared, so we get 100pi. But there are 3 circles, so we have 100pi + 100pi + 100pi. THat gets us 300pi. Now, subtract the total areas of the 3 circles from the rectangle, and we get: 1200 - 300pi. Otherwise known as D.

^_^

Answer 3

I got it its d

Answer 4

Nice.