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4. A water glass is shaped like a cylinder with height 9 in. and diameter 4 in. How many times as much water can a glass three times as tall and three times as wide hold? 27 113.1 A. 54 B. 27 C. 6 D. 36 12

4. A water glass is shaped like a cylinder with height 9 in. and diameter 4 in. How many times as much water can a glass three times as tall and three times as wide hold? 27 113.1 A. 54 B. 27 C. 6 D. 36 12

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Educational Material Transcription #### Geometry Examination **3.** The circumference of a circle is \(8\pi\) in. If the area is multiplied by 25, what happens to the radius? - A. It is increased by a factor of \(\frac{1}{5}\). - B. It is increased by a factor of 25. - C. It is increased by a factor of 5. - D. It is decreased by a factor of 5. **4.** A water glass is shaped like a cylinder with a height of \(9 \, \text{in.}\) and diameter \(4 \, \text{in.}\) How many times as much water can a glass three times as tall and three times as wide hold? - A. 54 - B. 27 - C. 6 - D. 36 _Diagram_: A cylinder with a height of 9 inches and a diameter of 4 inches is drawn. **5.** Find the area of this rectangle. _Diagram_: A rectangle is shown, having diagonal \(d = 12 \, \text{in.}\) and a length \(l = 10 \, \text{in.}\) - A. \(120 \, \text{in}^2\) - B. \(66.3 \, \text{in}^2\) - C. \(60 \, \text{in}^2\) - D. \(80.5 \, \text{in}^2\) ### Handwritten Mathematical Calculations **4.** Calculation for water glass volume: - Height \( = 9 \, \text{in.} \) - Diameter \( = 4 \, \text{in.} \) - Volume calculation: \(27 \times \pi \times (2)^2 = 113.1 \) **5.** Calculation for the area of the rectangle: - Given: \(d = 12\, \text{in.}\), \(l = 10\, \text{in.}\) - Formula used: \( A = l \sqrt{d^2 - l^2}\) - Calculations: \( A = 10 \sqrt{12^2 - 10^2} = 10 \sqrt{144 - 100} = 10 \sqrt{
Transcribed Image Text:### Educational Material Transcription #### Geometry Examination **3.** The circumference of a circle is \(8\pi\) in. If the area is multiplied by 25, what happens to the radius? - A. It is increased by a factor of \(\frac{1}{5}\). - B. It is increased by a factor of 25. - C. It is increased by a factor of 5. - D. It is decreased by a factor of 5. **4.** A water glass is shaped like a cylinder with a height of \(9 \, \text{in.}\) and diameter \(4 \, \text{in.}\) How many times as much water can a glass three times as tall and three times as wide hold? - A. 54 - B. 27 - C. 6 - D. 36 _Diagram_: A cylinder with a height of 9 inches and a diameter of 4 inches is drawn. **5.** Find the area of this rectangle. _Diagram_: A rectangle is shown, having diagonal \(d = 12 \, \text{in.}\) and a length \(l = 10 \, \text{in.}\) - A. \(120 \, \text{in}^2\) - B. \(66.3 \, \text{in}^2\) - C. \(60 \, \text{in}^2\) - D. \(80.5 \, \text{in}^2\) ### Handwritten Mathematical Calculations **4.** Calculation for water glass volume: - Height \( = 9 \, \text{in.} \) - Diameter \( = 4 \, \text{in.} \) - Volume calculation: \(27 \times \pi \times (2)^2 = 113.1 \) **5.** Calculation for the area of the rectangle: - Given: \(d = 12\, \text{in.}\), \(l = 10\, \text{in.}\) - Formula used: \( A = l \sqrt{d^2 - l^2}\) - Calculations: \( A = 10 \sqrt{12^2 - 10^2} = 10 \sqrt{144 - 100} = 10 \sqrt{
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