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In the figure above, the circumference of the circle is equal to , and
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09 Dec 2022, 06:20
09 Dec 2022, 06:20
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In the figure above, the circumference of the circle is equal to 1/4 , and the arc PQR is equal to 1/4 of the total circumference. What is the area of the shaded region?
16π − 16
2π − 8
8π − 8
4π − 8
4π
Re: In the figure above, the circumference of the circle is equal to , and
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11 Dec 2022, 04:00
11 Dec 2022, 04:00
Expert Reply
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For most shaded area problem, use the formula shaded area = total area − unshaded area. Since the figure for the problem does not include a center for the circle, give the circle a center O. Draw one radius from the center O to point P, and another radius from O to point R to create central angle POR. Since arc PQR equals 1/4 of the total circumference, the central angle formed will be 1/4 of 360°; angle PQR is 90°. From the information in the problem you know that circumference = 8π, so r = 4. The triangle POR is an isosceles right triangle with legs of 4 and an area of 8. The area of the circle is equal to πr2, so the area of the circle is 16π. The total area taken up by the triangle and the shaded area together will be equal to 1/4 of the area of the circle, or 4π. The total area is 4π and the unshaded area is 8, so the shaded area is 4π − 8, which is choice (D).
For most shaded area problem, use the formula shaded area = total area − unshaded area. Since the figure for the problem does not include a center for the circle, give the circle a center O. Draw one radius from the center O to point P, and another radius from O to point R to create central angle POR. Since arc PQR equals 1/4 of the total circumference, the central angle formed will be 1/4 of 360°; angle PQR is 90°. From the information in the problem you know that circumference = 8π, so r = 4. The triangle POR is an isosceles right triangle with legs of 4 and an area of 8. The area of the circle is equal to πr2, so the area of the circle is 16π. The total area taken up by the triangle and the shaded area together will be equal to 1/4 of the area of the circle, or 4π. The total area is 4π and the unshaded area is 8, so the shaded area is 4π − 8, which is choice (D).
Re: In the figure above, the circumference of the circle is equal to , and
[#permalink]
11 Dec 2022, 06:03
11 Dec 2022, 06:03
Hi,
How do you get circumference = 8π?
the circumference of the circle is equal to 1/4 , and the arc PQR is equal to 1/4 of the total circumference.
2πr = 1/4
r = 1/8π ?
How do you get circumference = 8π?
the circumference of the circle is equal to 1/4 , and the arc PQR is equal to 1/4 of the total circumference.
2πr = 1/4
r = 1/8π ?
