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32 Find the probability that a randomly selected point falls in the shaded region. 40:180 2% 10 18 4 10

32 Find the probability that a randomly selected point falls in the shaded region. 40:180 2% 10 18 4 10

Elementary Geometry For College Students, 7e
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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### Math Problems and Solutions #### Problem 31: **Question:** Find the lateral area of a regular square pyramid with base edge 20 cm and lateral edge 17 cm. **Options:** - A. \(120 \, \text{cm}^2\) - B. \(240 \, \text{cm}^2\) - C. \(550 \, \text{cm}^2\) - D. \(1020 \, \text{cm}^2\) #### Problem 32: **Question:** Find the probability that a randomly selected point falls in the shaded region. **Explanation:** The diagram shows two rectangles. The outer larger rectangle has dimensions labeled 18 and 10, while the smaller inner rectangle, which is shaded, has dimensions labeled 10 and 4. The numbers 40:180 and 22% are handwritten next to the diagram. **Options:** - A. 77.8% - B. 28.5% - C. 22.2% - D. 75.0% **Diagram Analysis:** The larger rectangle's area can be computed as 18 * 10 = 180 square units. The smaller rectangle's area can be computed as 10 * 4 = 40 square units. The probability that a point falls in the shaded area is the area of the shaded region divided by the area of the larger rectangle, which is \(\frac{40}{180} \approx 0.222\) or 22.2%. #### Problem 33: **Question:** Two similar cylinders have heights of 2 cm and 3 cm. What is the ratio of their volumes? **Options:** - A. \(\frac{4}{9}\) - B. \(\frac{8}{27}\) - C. \(\frac{2}{3}\) - D. \(\frac{1}{2}\) **Handwritten Notes:** The handwritten note "2/3" and the word "same" are included next to the options. **Explanation:** If two cylinders are similar, the ratio of their volumes is the cube of the ratio of their heights. Thus, the ratio of volumes is \(\left(\frac{2}{3}\right)^3 = \frac{8}{27}\). --- These problems focus on geometry and probability, requiring an understanding of lateral areas, probability calculation, and volume
Transcribed Image Text:### Math Problems and Solutions #### Problem 31: **Question:** Find the lateral area of a regular square pyramid with base edge 20 cm and lateral edge 17 cm. **Options:** - A. \(120 \, \text{cm}^2\) - B. \(240 \, \text{cm}^2\) - C. \(550 \, \text{cm}^2\) - D. \(1020 \, \text{cm}^2\) #### Problem 32: **Question:** Find the probability that a randomly selected point falls in the shaded region. **Explanation:** The diagram shows two rectangles. The outer larger rectangle has dimensions labeled 18 and 10, while the smaller inner rectangle, which is shaded, has dimensions labeled 10 and 4. The numbers 40:180 and 22% are handwritten next to the diagram. **Options:** - A. 77.8% - B. 28.5% - C. 22.2% - D. 75.0% **Diagram Analysis:** The larger rectangle's area can be computed as 18 * 10 = 180 square units. The smaller rectangle's area can be computed as 10 * 4 = 40 square units. The probability that a point falls in the shaded area is the area of the shaded region divided by the area of the larger rectangle, which is \(\frac{40}{180} \approx 0.222\) or 22.2%. #### Problem 33: **Question:** Two similar cylinders have heights of 2 cm and 3 cm. What is the ratio of their volumes? **Options:** - A. \(\frac{4}{9}\) - B. \(\frac{8}{27}\) - C. \(\frac{2}{3}\) - D. \(\frac{1}{2}\) **Handwritten Notes:** The handwritten note "2/3" and the word "same" are included next to the options. **Explanation:** If two cylinders are similar, the ratio of their volumes is the cube of the ratio of their heights. Thus, the ratio of volumes is \(\left(\frac{2}{3}\right)^3 = \frac{8}{27}\). --- These problems focus on geometry and probability, requiring an understanding of lateral areas, probability calculation, and volume
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