Question

lesson # 14: solve and draw - circles: circumference and area

1. the radius (r) is a line from the center of a circle to a point on the circle. how long is this radius? 10
2. the diameter (d) is the distance across a circle through its center point. how long is the diameter? 20
3. circumference is the distance around a circle. finding this length uses π. let π = 3.14. to find the circumference, use the formula c = d×π. whats the circumference if d = 12?
4. to find the area of a circle, use the formula a = πr². whats the approximate area of a circle with a radius of 8 ft.?
5. the diameter of a circle is 20. whats the area of the circle?
6. the diameter of a circle is 16m. what is the circumference?
7. a circular rug has a diameter of 12 feet. whats the approximate area of the rug?
8. the radius of a circular platter is 10in. find the circumference.
9. the diameter of a circular pizza is 24 in. how much pizza is eaten (in square inches) if half of it is consumed? (pie and π... hmmmm... interesting...)

Explanation:

1. Question 4: Area of a circle with \(r = 8\) ft

• # Explanation:
• ## Step1: Recall the area - formula
• The formula for the area of a circle is \(A=\pi r^{2}\), where \(r\) is the radius of the circle and \(\pi\approx3.14\).
• ## Step2: Substitute the value of \(r\)
• Substitute \(r = 8\) into the formula: \(A=3.14\times8^{2}=3.14\times64 = 200.96\approx200\) \(ft^{2}\).
• # Answer:
• about \(200\) \(ft^{2}\)

1. Question 5: Area of a circle with \(d = 20\)

• First, find the radius. Since \(d = 2r\), then \(r=\frac{d}{2}=\frac{20}{2}=10\).
• # Explanation:
• ## Step1: Recall the area - formula
• The formula for the area of a circle is \(A=\pi r^{2}\), with \(\pi\approx3.14\).
• ## Step2: Substitute the value of \(r\)
• Substitute \(r = 10\) into the formula: \(A = 3.14\times10^{2}=3.14\times100=314\) \(u^{2}\).
• # Answer:
• \(314\) \(u^{2}\)

1. Question 6: Circumference of a circle with \(d = 16\) m

• # Explanation:
• ## Step1: Recall the circumference - formula
• The formula for the circumference of a circle is \(C=\pi d\), where \(d\) is the diameter and \(\pi\approx3.14\).
• ## Step2: Substitute the value of \(d\)
• Substitute \(d = 16\) into the formula: \(C=3.14\times16 = 50.24\) m.
• # Answer:
• \(C = 50.24\) m

1. Question 7: Area of a circular rug with \(d = 12\) ft

• First, find the radius. Since \(d = 2r\), then \(r=\frac{d}{2}=\frac{12}{2}=6\) ft.
• # Explanation:
• ## Step1: Recall the area - formula
• The formula for the area of a circle is \(A=\pi r^{2}\), with \(\pi\approx3.14\).
• ## Step2: Substitute the value of \(r\)
• Substitute \(r = 6\) into the formula: \(A=3.14\times6^{2}=3.14\times36 = 113.04\approx113\) \(ft^{2}\).
• # Answer:
• \(113\) \(ft^{2}\)

1. Question 8: Circumference of a circular platter with \(r = 10\) in

• # Explanation:
• ## Step1: Recall the circumference - formula
• The formula for the circumference of a circle is \(C = 2\pi r\), with \(\pi\approx3.14\).
• ## Step2: Substitute the value of \(r\)
• Substitute \(r = 10\) into the formula: \(C=2\times3.14\times10=62.8\) in.
• # Answer:
• \(C = 62.8\) in

1. Question 9: Area of half - a pizza with \(d = 24\) in

• First, find the radius. Since \(d = 2r\), then \(r=\frac{d}{2}=\frac{24}{2}=12\) in.
• The area of the whole pizza is \(A=\pi r^{2}\), with \(\pi\approx3.14\).
• # Explanation:
• ## Step1: Find the area of the whole pizza
• Substitute \(r = 12\) into the formula \(A=\pi r^{2}\): \(A = 3.14\times12^{2}=3.14\times144 = 452.16\) \(in^{2}\).
• ## Step2: Find the area of half - the pizza
• The area of half - the pizza is \(\frac{A}{2}=\frac{452.16}{2}=226.08\) \(in^{2}\).
• # Answer:
• \(226.08\) \(in^{2}\)

Answer:

1. Question 4: Area of a circle with \(r = 8\) ft

• # Explanation:
• ## Step1: Recall the area - formula
• The formula for the area of a circle is \(A=\pi r^{2}\), where \(r\) is the radius of the circle and \(\pi\approx3.14\).
• ## Step2: Substitute the value of \(r\)
• Substitute \(r = 8\) into the formula: \(A=3.14\times8^{2}=3.14\times64 = 200.96\approx200\) \(ft^{2}\).
• # Answer:
• about \(200\) \(ft^{2}\)

1. Question 5: Area of a circle with \(d = 20\)

• First, find the radius. Since \(d = 2r\), then \(r=\frac{d}{2}=\frac{20}{2}=10\).
• # Explanation:
• ## Step1: Recall the area - formula
• The formula for the area of a circle is \(A=\pi r^{2}\), with \(\pi\approx3.14\).
• ## Step2: Substitute the value of \(r\)
• Substitute \(r = 10\) into the formula: \(A = 3.14\times10^{2}=3.14\times100=314\) \(u^{2}\).
• # Answer:
• \(314\) \(u^{2}\)

1. Question 6: Circumference of a circle with \(d = 16\) m

• # Explanation:
• ## Step1: Recall the circumference - formula
• The formula for the circumference of a circle is \(C=\pi d\), where \(d\) is the diameter and \(\pi\approx3.14\).
• ## Step2: Substitute the value of \(d\)
• Substitute \(d = 16\) into the formula: \(C=3.14\times16 = 50.24\) m.
• # Answer:
• \(C = 50.24\) m

1. Question 7: Area of a circular rug with \(d = 12\) ft

• First, find the radius. Since \(d = 2r\), then \(r=\frac{d}{2}=\frac{12}{2}=6\) ft.
• # Explanation:
• ## Step1: Recall the area - formula
• The formula for the area of a circle is \(A=\pi r^{2}\), with \(\pi\approx3.14\).
• ## Step2: Substitute the value of \(r\)
• Substitute \(r = 6\) into the formula: \(A=3.14\times6^{2}=3.14\times36 = 113.04\approx113\) \(ft^{2}\).
• # Answer:
• \(113\) \(ft^{2}\)

1. Question 8: Circumference of a circular platter with \(r = 10\) in

• # Explanation:
• ## Step1: Recall the circumference - formula
• The formula for the circumference of a circle is \(C = 2\pi r\), with \(\pi\approx3.14\).
• ## Step2: Substitute the value of \(r\)
• Substitute \(r = 10\) into the formula: \(C=2\times3.14\times10=62.8\) in.
• # Answer:
• \(C = 62.8\) in

1. Question 9: Area of half - a pizza with \(d = 24\) in

• First, find the radius. Since \(d = 2r\), then \(r=\frac{d}{2}=\frac{24}{2}=12\) in.
• The area of the whole pizza is \(A=\pi r^{2}\), with \(\pi\approx3.14\).
• # Explanation:
• ## Step1: Find the area of the whole pizza
• Substitute \(r = 12\) into the formula \(A=\pi r^{2}\): \(A = 3.14\times12^{2}=3.14\times144 = 452.16\) \(in^{2}\).
• ## Step2: Find the area of half - the pizza
• The area of half - the pizza is \(\frac{A}{2}=\frac{452.16}{2}=226.08\) \(in^{2}\).
• # Answer:
• \(226.08\) \(in^{2}\)