Question

1. solve the word problem. pietro is planning a patio using paving stones that are circles, semicircles, and quarter - circles. all stones have a radius of 10 inches. what is the area of one pattern of stones that has 5 circles, 10 semicircles, and 100 quarter - circles? then, select the total area. 10 semicircles = 1,570 in² total area = 8,164 in² 10 semicircles = 2,198 in² 100 quarter circles = 2,826 in² 5 circles = 2,198 in² 5 circles = 1,570 in² total area = 10,990 in² 100 quarter - circles = 7,850 in²

Explanation:

Step1: Calculate full circle area

Area of 1 full circle: $\pi r^2 = \pi (10)^2 = 100\pi \approx 314$ in²

Step2: Calculate 5 circles area

Total area for 5 circles: $5 \times 314 = 1570$ in²

Step3: Calculate 1 semicircle area

Area of 1 semicircle: $\frac{1}{2} \times 100\pi = 50\pi \approx 157$ in²

Step4: Calculate 10 semicircles area

Total area for 10 semicircles: $10 \times 157 = 1570$ in²

Step5: Calculate 1 quarter-circle area

Area of 1 quarter-circle: $\frac{1}{4} \times 100\pi = 25\pi \approx 78.5$ in²

Step6: Calculate 100 quarter-circles area

Total area for 100 quarter-circles: $100 \times 78.5 = 7850$ in²

Step7: Calculate total pattern area

Sum all individual areas: $1570 + 1570 + 7850 = 10990$ in²

Answer:

$\square$ 5 circles = 1,570 in²
$\square$ 10 semicircles = 1,570 in²
$\square$ 100 quarter-circles = 7,850 in²
$\square$ total area = 10,990 in²