Question
Question A cylinder has a base diameter of 4 feet and a height of 13 feet. What is its volume in cubic feet, to the nearest tenths place?
Ask by Schultz Davison. in the United States
Jan 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The cylinder's volume is approximately 163.4 cubic feet.
Solution
To find the volume of a cylinder, use the formula:
\[
\text{Volume} = \pi r^2 h
\]
Where:
- \( r \) is the radius of the base
- \( h \) is the height of the cylinder
**Given:**
- Diameter of the base = 4 feet, so the radius \( r = \frac{4}{2} = 2 \) feet
- Height \( h = 13 \) feet
**Calculate the Volume:**
\[
\text{Volume} = \pi \times (2)^2 \times 13 = \pi \times 4 \times 13 = 52\pi
\]
Using \( \pi \approx 3.1416 \):
\[
\text{Volume} \approx 52 \times 3.1416 \approx 163.3628 \, \text{cubic feet}
\]
**Rounded to the nearest tenths place:**
\[
\text{Volume} \approx 163.4 \, \text{cubic feet}
\]
**Answer:**
The cylinder’s volume is approximately 163.4 cubic feet.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
To find the volume of the cylinder, you can use the formula: V = πr²h, where r is the radius and h is the height. First, calculate the radius by dividing the diameter by 2. So, r = 4 ft / 2 = 2 ft. Plugging in the values: V = π(2 ft)²(13 ft) = π(4 ft²)(13 ft) = 52π ft³. Approximating π as 3.14 gives you a volume of about 163.4 cubic feet when rounded to the nearest tenth. So, the volume of the cylinder is approximately 163.4 cubic feet.
