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

A pattern for Miata’s new carpet design contains circles, semicircles, and quarter-circles. All circular shapes have a radius of 8 cm. What is the area of a pattern that contains 1 circle, 4 semicircles, and 8 quarter-circles? There should be four answers

Area of circle: _____
Area of semicircles: _____
Area of quarter-circles: _____
Total area of pattern: _____

Area of semicircles

Area of semicircles =

Area of circle =

Area of quarter-circles =

Total area of pattern

Area of quarter-circles

Area of circle

Total area of pattern

Respuesta :

Answer:

1)Area of circle: 64[tex]\pi[/tex]

2)Area of semicircles: 128[tex]\pi[/tex]

3)Area of quarter-circles: 128[tex]\pi[/tex]

4)Total area of pattern: 320[tex]\pi[/tex]

Step-by-step explanation:

r = 8cm

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

Area of a circle: [tex]\pi r^{2}[/tex]

1) A = [tex]\pi r^{2}[/tex] where r = 8

A = 64[tex]\pi[/tex]

2) 4 semicircles = 2 circles

so the answer is 2*A = 128[tex]\pi[/tex]

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 [tex]\frac{1}{2}[/tex] 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[tex]\pi[/tex]