Question

Solve the word problem. Round your final result to the nearest hundredth.

Answer 1

Answer:

1)Area of circle: 64$\pi$

2)Area of semicircles: 128$\pi$

3)Area of quarter-circles: 128$\pi$

4)Total area of pattern: 320$\pi$

Step-by-step explanation:

r = 8cm

Given: 1 circle, 4 semicircles, and 8 quarter-circles.

Area of a circle: $\pi r^{2}$

1) A = $\pi r^{2}$ where r = 8

A = 64$\pi$

2) 4 semicircles = 2 circles

so the answer is 2*A = 128$\pi$

3) 8 quarter-circles = 2 circles

Therefore, the answer here is the same as the answer for #2!

4)There are 5 circles total because:

1 circle = 1 circle

4 semicircles divided by 2 = 2 circles (because $\frac{1}{2}$ times 4)

8 quarter-circles divided by 4 (think about what "quarter" means) = 2 circles

So ... 1 + 2 + 2 = 5 circles

Now we need to find the area of 5 circles which is just 5*A

5*A = 320$\pi$