sel in St. Augustine Park has a diameter of 36 feet. Each ride lasts 3 minutes and the speed of th s per minute. What is the maximum distance riders travel in one full ride? Round to the nearest h
sel in St. Augustine Park has a diameter of 36 feet. Each ride lasts 3 minutes and the speed of th s per minute. What is the maximum distance riders travel in one full ride? Round to the nearest h
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
Related questions
Question
![**Problem Statement:**
The carousel in St. Augustine Park has a diameter of 36 feet. Each ride lasts 3 minutes and the speed of the carousel is 3.8 revolutions per minute. What is the maximum distance riders travel in one full ride? Round to the nearest hundredth.
**Calculation:**
1. **Find the circumference of the carousel:**
The formula to calculate the circumference (C) is:
\[
C = \pi \times \text{diameter}
\]
Given the diameter is 36 feet:
\[
C = \pi \times 36 \approx 113.1 \, \text{feet}
\]
2. **Calculate the total number of revolutions in one ride:**
Each ride lasts 3 minutes with a speed of 3.8 revolutions per minute:
\[
\text{Total revolutions} = 3 \, \text{minutes} \times 3.8 \, \text{rev/min} = 11.4 \, \text{revolutions}
\]
3. **Compute the maximum distance traveled:**
Maximum distance is the product of the total number of revolutions and the circumference:
\[
\text{Maximum distance} = 11.4 \, \text{revolutions} \times 113.1 \, \text{feet/revolution} \approx 1289.34 \, \text{feet}
\]
**Result:**
The maximum distance is **1289.34 feet**.
**Interactive Input:**
To answer, fill in the blank provided below:
The maximum distance is ________ feet.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae536b8e-4270-4156-acbd-83b6e6d1cf9d%2Fa336dad9-1468-4881-8e9a-e926347901b8%2Fcjbe59_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
The carousel in St. Augustine Park has a diameter of 36 feet. Each ride lasts 3 minutes and the speed of the carousel is 3.8 revolutions per minute. What is the maximum distance riders travel in one full ride? Round to the nearest hundredth.
**Calculation:**
1. **Find the circumference of the carousel:**
The formula to calculate the circumference (C) is:
\[
C = \pi \times \text{diameter}
\]
Given the diameter is 36 feet:
\[
C = \pi \times 36 \approx 113.1 \, \text{feet}
\]
2. **Calculate the total number of revolutions in one ride:**
Each ride lasts 3 minutes with a speed of 3.8 revolutions per minute:
\[
\text{Total revolutions} = 3 \, \text{minutes} \times 3.8 \, \text{rev/min} = 11.4 \, \text{revolutions}
\]
3. **Compute the maximum distance traveled:**
Maximum distance is the product of the total number of revolutions and the circumference:
\[
\text{Maximum distance} = 11.4 \, \text{revolutions} \times 113.1 \, \text{feet/revolution} \approx 1289.34 \, \text{feet}
\]
**Result:**
The maximum distance is **1289.34 feet**.
**Interactive Input:**
To answer, fill in the blank provided below:
The maximum distance is ________ feet.
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