2. Leonore is making a quilt with circles stitched together. The circles all have los° -6.2 in: 16in a diameter of 16 inches. In order for the quilt to have straight edges, she must 10.2 in. cut off the portion of the circular fabric that is shaded in the diagram for the border pieces. The measure of the central angle is 105°. How much surface area of the border pieces will she lose when she removes this part of the fabric piece? Use 3.14 for n and round your answer to the nearest hundredth if necessary.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Problem 2:**

Leonore is making a quilt with circles stitched together. The circles all have a diameter of 16 inches. To achieve straight edges on the quilt, she must cut off the portion of the circular fabric that is shaded in the diagram for the border pieces.

**Diagram Explanation:**
- The diagram shows a circle with a shaded sector.
- The diameter of the circle is labeled as 16 inches.
- The radius of the circle, half the diameter, is 8 inches, as indicated by the label "10.2 in." pointing to the circle's radius.
- A central angle measuring 105° is shown, which subtends the shaded area of the sector.
- The shaded area to be removed is indicated explicitly.

**Task:**
Calculate how much surface area of the border pieces she will lose by removing the shaded part of the fabric. Use 3.14 for π (pi), and round your answer to the nearest hundredth if necessary.
Transcribed Image Text:**Problem 2:** Leonore is making a quilt with circles stitched together. The circles all have a diameter of 16 inches. To achieve straight edges on the quilt, she must cut off the portion of the circular fabric that is shaded in the diagram for the border pieces. **Diagram Explanation:** - The diagram shows a circle with a shaded sector. - The diameter of the circle is labeled as 16 inches. - The radius of the circle, half the diameter, is 8 inches, as indicated by the label "10.2 in." pointing to the circle's radius. - A central angle measuring 105° is shown, which subtends the shaded area of the sector. - The shaded area to be removed is indicated explicitly. **Task:** Calculate how much surface area of the border pieces she will lose by removing the shaded part of the fabric. Use 3.14 for π (pi), and round your answer to the nearest hundredth if necessary.
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