Alex has a bucket in the shape of a cylinder. The diameter of the bucket is 12 inches and its height is 11.25 inches. How many buckets would it take to fill an empty aquarium with 65 gallons of water? Show your work. Enter your answer and work in the space provided.
Alex has a bucket in the shape of a cylinder. The diameter of the bucket is 12 inches and its height is 11.25 inches. How many buckets would it take to fill an empty aquarium with 65 gallons of water? Show your work. Enter your answer and work in the space provided.
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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Transcribed Image Text:**Problem Description:**
Part C
Alex has a bucket in the shape of a cylinder. The diameter of the bucket is 12 inches and its height is 11.25 inches. How many buckets would it take to fill an empty aquarium with 65 gallons of water? Show your work.
**Solution Space:**
- Answer box to enter calculations and final answer.
**Tools Provided:**
- Math Symbols: Includes basic operations (addition, subtraction, multiplication, division), fraction editor, exponents, square root, pi, and more.
- Relations: Can be expanded for additional mathematical relations.
- Geometry: Can be expanded for geometric figures and relations.
To solve the problem:
1. **Calculate the Volume of the Bucket in Cubic Inches:**
- Formula for the volume of a cylinder: \( V = \pi r^2 h \)
- Given, diameter = 12 inches, so radius \( r = \frac{12}{2} = 6 \) inches.
- Height \( h = 11.25 \) inches.
\( V = \pi \times 6^2 \times 11.25 \)
2. **Convert Volume from Cubic Inches to Gallons:**
- 1 gallon = 231 cubic inches.
- Calculate number of buckets needed by converting volume of the aquarium from gallons to cubic inches and dividing by volume of one bucket.
3. **Final Calculation:**
- Determine how many buckets are needed to fill the aquarium by dividing the total volume in cubic inches by the volume of the bucket.
![Alex bought a new aquarium. He is in the process of setting it up. The aquarium is in the shape of a right rectangular prism and the dimensions, in inches, are \(36 \frac{7}{8} \times 19 \times 24 \frac{5}{8}\).
During the set-up, Alex fills the aquarium with \(6,039 \, \text{in}^3\) of water.
**Part A**
What percent of the volume of the aquarium is filled with water? Round your answer to the nearest whole percent.
Enter your answer in the space provided.
\[ \boxed{35} \% \]
**Part B**
The aquarium is advertised as being able to hold a maximum of 65 gallons of water as the aquarium is not meant to be completely filled with water. Assume Alex fills the aquarium to its maximum capacity. Based on the dimensions of the aquarium, what percent of the aquarium should not be filled with water? Round your answer to the nearest whole percent.
1 gallon = 231 cubic inches
Enter your answer in the space provided.
\[ \boxed{} \% \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9f378aa-3d9e-44fe-8691-e65fc073f1a6%2Fe82af9b7-ebde-44fd-9da0-adf97a2c63ef%2Fc0wc88h_processed.png&w=3840&q=75)
Transcribed Image Text:Alex bought a new aquarium. He is in the process of setting it up. The aquarium is in the shape of a right rectangular prism and the dimensions, in inches, are \(36 \frac{7}{8} \times 19 \times 24 \frac{5}{8}\).
During the set-up, Alex fills the aquarium with \(6,039 \, \text{in}^3\) of water.
**Part A**
What percent of the volume of the aquarium is filled with water? Round your answer to the nearest whole percent.
Enter your answer in the space provided.
\[ \boxed{35} \% \]
**Part B**
The aquarium is advertised as being able to hold a maximum of 65 gallons of water as the aquarium is not meant to be completely filled with water. Assume Alex fills the aquarium to its maximum capacity. Based on the dimensions of the aquarium, what percent of the aquarium should not be filled with water? Round your answer to the nearest whole percent.
1 gallon = 231 cubic inches
Enter your answer in the space provided.
\[ \boxed{} \% \]
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