Asked by miya
Jaylon created thisstained-glass window.The upper two corners arequarter circles, each with aradius of 4 inches. Find thearea of the window. Use3.14 formath
π
.
A diagram of a stained-glass window.
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<ul> <li>The bottom part of the window is a rectangle with the bottom, shorter, side 12 inches.</li> <li>The top right and left corners are quarter-circles with radius 4 inches.</li> <li>There is an unmeasured part of the window between the quarter-circles.</li> <li>The total height of the window is 26 inches.</ul>
The circumference of a circle is 50.24 meters.What is the area of the circle? Use 3.14 formath
π
.
Higher Order ThinkingA circular flower bed is20 meters in diameter and has a circular sidewalkaround it that is 3 meters wide. Find the area ofthe sidewalk in square meters. Use 3.14 formath
π
.Round to the nearest whole number.
A circular plate has a circumference of16.3 inches. What is the area of thisplate? Use 3.14 formath
π
. Round to the nearestwhole number.
A water sprinkler sends water out in a circular pattern. How many feetaway from the sprinkler can it spread water if the area formed by thewatering pattern is 379.94 square feet?
All Answers 1
Answered by
GPT-5 mini
AI
1) Stained-glass window
- Interpret the window as a 12 in × 26 in rectangle with the two upper corners removed as quarter-circles of radius 4 in. The two quarters together equal a half-circle of radius 4.
- Rectangle area = 12 × 26 = 312 in².
- Half-circle area = (1/2)π(4²) = 0.5 × 3.14 × 16 = 25.12 in².
- Window area = 312 − 25.12 = 286.88 in².
Answer: 286.88 in²
2) Circumference = 50.24 m → area?
- r = C/(2π) = 50.24/(2 × 3.14) = 8 m.
- Area = πr² = 3.14 × 8² = 3.14 × 64 = 200.96 m².
Answer: 200.96 m²
3) Higher order thinking — flower bed and sidewalk
- Inner radius = 20/2 = 10 m; outer radius = 10 + 3 = 13 m.
- Sidewalk area = π(13² − 10²) = 3.14 × (169 − 100) = 3.14 × 69 = 216.66 m².
- Rounded to nearest whole number: 217 m².
Answer: 217 m²
4) Circular plate: circumference 16.3 in → area?
- r = 16.3/(2 × 3.14) ≈ 2.59554 in.
- Area = 3.14 × r² ≈ 3.14 × (2.59554)² ≈ 21.17 in².
- Rounded to nearest whole number: 21 in².
Answer: 21 in²
5) Sprinkler: area = 379.94 ft² → how far can water spread?
- r = sqrt(area/π) = sqrt(379.94/3.14) = sqrt(121) = 11 ft.
Answer: 11 ft
- Interpret the window as a 12 in × 26 in rectangle with the two upper corners removed as quarter-circles of radius 4 in. The two quarters together equal a half-circle of radius 4.
- Rectangle area = 12 × 26 = 312 in².
- Half-circle area = (1/2)π(4²) = 0.5 × 3.14 × 16 = 25.12 in².
- Window area = 312 − 25.12 = 286.88 in².
Answer: 286.88 in²
2) Circumference = 50.24 m → area?
- r = C/(2π) = 50.24/(2 × 3.14) = 8 m.
- Area = πr² = 3.14 × 8² = 3.14 × 64 = 200.96 m².
Answer: 200.96 m²
3) Higher order thinking — flower bed and sidewalk
- Inner radius = 20/2 = 10 m; outer radius = 10 + 3 = 13 m.
- Sidewalk area = π(13² − 10²) = 3.14 × (169 − 100) = 3.14 × 69 = 216.66 m².
- Rounded to nearest whole number: 217 m².
Answer: 217 m²
4) Circular plate: circumference 16.3 in → area?
- r = 16.3/(2 × 3.14) ≈ 2.59554 in.
- Area = 3.14 × r² ≈ 3.14 × (2.59554)² ≈ 21.17 in².
- Rounded to nearest whole number: 21 in².
Answer: 21 in²
5) Sprinkler: area = 379.94 ft² → how far can water spread?
- r = sqrt(area/π) = sqrt(379.94/3.14) = sqrt(121) = 11 ft.
Answer: 11 ft
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