44. The area formula for a regular polygon is ap. Find the area of a regular 2 pentagon with side length 15 cm and apothem 10 cm. A. 750 cm² B. 375 cm² C. 900 cm² D. 450 cm² 45. Sphere B has 9 times the surface area of sphere A. How many times the volume of sphere A is the volume of sphere B? A. 9 B. 27 C. 9 D. 27 46. Find the area of this trapezoid using A=h(b₁ + b₂) 9 ft 11 ft A 7 ft FRE 9x B of 094 to 8 aut al ainen ni 0 euiban riw
44. The area formula for a regular polygon is ap. Find the area of a regular 2 pentagon with side length 15 cm and apothem 10 cm. A. 750 cm² B. 375 cm² C. 900 cm² D. 450 cm² 45. Sphere B has 9 times the surface area of sphere A. How many times the volume of sphere A is the volume of sphere B? A. 9 B. 27 C. 9 D. 27 46. Find the area of this trapezoid using A=h(b₁ + b₂) 9 ft 11 ft A 7 ft FRE 9x B of 094 to 8 aut al ainen ni 0 euiban riw
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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![### Geometry Problems
Below are some geometry problems designed to help students practice calculating areas and volumes of various shapes.
#### Problem 44
**Question:**
The area formula for a regular polygon is \( \frac{1}{2}ap \). Find the area of a regular pentagon with side length 15 cm and apothem 10 cm.
**Options:**
- A. 750 cm²
- B. 375 cm²
- C. 900 cm²
- D. 450 cm²
**Explanation:**
Here, \( a = \) apothem = 10 cm,
\( p = \) perimeter = 5 × 15 cm = 75 cm.
Using the formula for the area of a regular polygon:
\[ \text{Area} = \frac{1}{2} \times 10 \times 75 = 375 \, \text{cm}² \]
The correct answer is:
- **B. 375 cm²**
#### Problem 45
**Question:**
Sphere \( B \) has 9 times the surface area of sphere \( A \). How many times the volume of sphere \( A \) is the volume of sphere \( B \)?
**Options:**
- A. 9
- B. \(27\pi\)
- C. \(9\pi\)
- D. 27
**Explanation:**
If Sphere \( B \) has 9 times the surface area of Sphere \( A \), then the ratio of their radii will be \( \sqrt{9} = 3 \).
The volume ratio will be \(3^3 = 27 \).
The correct answer is:
- **D. 27**
#### Problem 46
**Question:**
Find the area of this trapezoid using \( A = \frac{1}{2}h(b_1 + b_2) \).
The given dimensions are:
- Height \( h = 9 \, \text{ft} \)
- Base 1 \( b_1 = 7 \, \text{ft} \)
- Base 2 \( b_2 = 11 \, \text{ft} \)
**Explanation:**
Applying the formula to find the area:
\[ \text{Area} = \frac{1}{2} \times 9 \times (7 + 11) \]
\[ \text](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d544791-a77c-4b5e-888b-2e8a4014205c%2Fb55bc14d-80ca-453f-b62e-2a97161efb66%2Fveo0svk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problems
Below are some geometry problems designed to help students practice calculating areas and volumes of various shapes.
#### Problem 44
**Question:**
The area formula for a regular polygon is \( \frac{1}{2}ap \). Find the area of a regular pentagon with side length 15 cm and apothem 10 cm.
**Options:**
- A. 750 cm²
- B. 375 cm²
- C. 900 cm²
- D. 450 cm²
**Explanation:**
Here, \( a = \) apothem = 10 cm,
\( p = \) perimeter = 5 × 15 cm = 75 cm.
Using the formula for the area of a regular polygon:
\[ \text{Area} = \frac{1}{2} \times 10 \times 75 = 375 \, \text{cm}² \]
The correct answer is:
- **B. 375 cm²**
#### Problem 45
**Question:**
Sphere \( B \) has 9 times the surface area of sphere \( A \). How many times the volume of sphere \( A \) is the volume of sphere \( B \)?
**Options:**
- A. 9
- B. \(27\pi\)
- C. \(9\pi\)
- D. 27
**Explanation:**
If Sphere \( B \) has 9 times the surface area of Sphere \( A \), then the ratio of their radii will be \( \sqrt{9} = 3 \).
The volume ratio will be \(3^3 = 27 \).
The correct answer is:
- **D. 27**
#### Problem 46
**Question:**
Find the area of this trapezoid using \( A = \frac{1}{2}h(b_1 + b_2) \).
The given dimensions are:
- Height \( h = 9 \, \text{ft} \)
- Base 1 \( b_1 = 7 \, \text{ft} \)
- Base 2 \( b_2 = 11 \, \text{ft} \)
**Explanation:**
Applying the formula to find the area:
\[ \text{Area} = \frac{1}{2} \times 9 \times (7 + 11) \]
\[ \text
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