8. Use Euler's Formula to find the number of vertices in the polyhedron with 8 to sens faces, 6 rectangles and 2 hexagons. A. 8 B. 12 C. 24 D. 18 9. What is the surface area, in square centimeters, of a sphere with radius 5 cm? A. 1000 2 B. 500 3 C. 100 D. 314 A=47/r² A. 6:10 B. 9:15 C. 9:25 D. 27: 125 4 (319) (5²) diy biosoqet a to se ni 8 lo 314.16 10. What is the ratio of the surface areas of similar solids whose similarity ratio is 3:5?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
#8
### Mathematics Problems for Educational Purposes

#### Problem 8:
Utilize Euler's Formula to determine the number of vertices in a polyhedron comprising 8 faces, 6 rectangles, and 2 hexagons.
- A. 8
- B. 12
- C. 24
- D. 18

#### Problem 9:
Calculate the surface area, in square centimeters, of a sphere with a radius of 5 cm.
- A. \( 1000\pi \)
- B. \( \frac{500\pi}{3} \)
- C. \( 100\pi \)
- D. \( 314\pi \)

Shown below the problem is a handwritten solution:
- Formula used: \( A = 4\pi r^2 \)
- Calculation: \( \text{Given: } r = 5 \, \text{cm} \)
  \( A = 4 \times \pi \times (5)^2 = 4 \times (3.14) \times (5)^2 \)
  \( 3.14 \times 25 = 314.16 \)

#### Problem 10:
Determine the ratio of the surface areas of similar solids whose similarity ratio is \( 3:5 \).
- A. \( 6 : 10 \)
- B. \( 9 : 15 \)
- C. \( 9 : 25 \)
- D. \( 27 : 125 \)

Explanation for diagrams/graphs: 
- There are no diagrams or graphs present in the image.
Transcribed Image Text:### Mathematics Problems for Educational Purposes #### Problem 8: Utilize Euler's Formula to determine the number of vertices in a polyhedron comprising 8 faces, 6 rectangles, and 2 hexagons. - A. 8 - B. 12 - C. 24 - D. 18 #### Problem 9: Calculate the surface area, in square centimeters, of a sphere with a radius of 5 cm. - A. \( 1000\pi \) - B. \( \frac{500\pi}{3} \) - C. \( 100\pi \) - D. \( 314\pi \) Shown below the problem is a handwritten solution: - Formula used: \( A = 4\pi r^2 \) - Calculation: \( \text{Given: } r = 5 \, \text{cm} \) \( A = 4 \times \pi \times (5)^2 = 4 \times (3.14) \times (5)^2 \) \( 3.14 \times 25 = 314.16 \) #### Problem 10: Determine the ratio of the surface areas of similar solids whose similarity ratio is \( 3:5 \). - A. \( 6 : 10 \) - B. \( 9 : 15 \) - C. \( 9 : 25 \) - D. \( 27 : 125 \) Explanation for diagrams/graphs: - There are no diagrams or graphs present in the image.
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