Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter62: Volumes Of Prisms And Cylinders
Section: Chapter Questions
Problem 38A: A copper casting is in the shape of a prism with an equilateral triangle base. The length of each...
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![### Trapezoid Area and Circle Similarity Ratio Calculations
#### Problem 14:
**Question:** What is the area of this trapezoid?
There is a diagram of a trapezoid with the following dimensions:
- One base is 7 meters
- The other base is 4 meters
- The height is 5 meters
To calculate the area of the trapezoid, use the formula:
\[ A = \frac{1}{2} \times (a + b) \times h \]
\[ A = \frac{1}{2} \times (7 + 4) \times 5 \]
\[ A = \frac{1}{2} \times 11 \times 5 \]
\[ A = \frac{55}{2} \]
\[ A = 27.5 \, m^2 \]
However, the options given are:
A. 21 m²
B. 27 m²
C. 26 m²
D. 29 m²
The correct choice is the closest to our calculated value:
- **Answer: B. 27 m²**
#### Problem 15:
**Question:** What is the area of a trapezoid with bases 8 and 18.5 inches, legs of 10 and 6.5 inches, and height of 6 inches?
To calculate the area, use the same formula for the area of a trapezoid:
\[ A = \frac{1}{2} \times (a + b) \times h \]
\[ A = \frac{1}{2} \times (8 + 18.5) \times 6 \]
\[ A = \frac{1}{2} \times 26.5 \times 6 \]
\[ A = \frac{1}{2} \times 159 \]
\[ A = 79.5 \, in^2 \]
The options given are:
A. 75 in²
B. 43 in²
C. 79.5 in²
D. 159 in²
- **Answer: C. 79.5 in²**
#### Problem 16:
**Question:** Find the similarity ratio of two circles with areas \(32\pi \, cm^2 \) and \(98\pi \, cm^2\).
The ratio of the areas of circles is equal to the square of the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d544791-a77c-4b5e-888b-2e8a4014205c%2Fec58ecf8-816c-4ba2-81db-3378d3f9a200%2Fkv5u5xe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Trapezoid Area and Circle Similarity Ratio Calculations
#### Problem 14:
**Question:** What is the area of this trapezoid?
There is a diagram of a trapezoid with the following dimensions:
- One base is 7 meters
- The other base is 4 meters
- The height is 5 meters
To calculate the area of the trapezoid, use the formula:
\[ A = \frac{1}{2} \times (a + b) \times h \]
\[ A = \frac{1}{2} \times (7 + 4) \times 5 \]
\[ A = \frac{1}{2} \times 11 \times 5 \]
\[ A = \frac{55}{2} \]
\[ A = 27.5 \, m^2 \]
However, the options given are:
A. 21 m²
B. 27 m²
C. 26 m²
D. 29 m²
The correct choice is the closest to our calculated value:
- **Answer: B. 27 m²**
#### Problem 15:
**Question:** What is the area of a trapezoid with bases 8 and 18.5 inches, legs of 10 and 6.5 inches, and height of 6 inches?
To calculate the area, use the same formula for the area of a trapezoid:
\[ A = \frac{1}{2} \times (a + b) \times h \]
\[ A = \frac{1}{2} \times (8 + 18.5) \times 6 \]
\[ A = \frac{1}{2} \times 26.5 \times 6 \]
\[ A = \frac{1}{2} \times 159 \]
\[ A = 79.5 \, in^2 \]
The options given are:
A. 75 in²
B. 43 in²
C. 79.5 in²
D. 159 in²
- **Answer: C. 79.5 in²**
#### Problem 16:
**Question:** Find the similarity ratio of two circles with areas \(32\pi \, cm^2 \) and \(98\pi \, cm^2\).
The ratio of the areas of circles is equal to the square of the
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