Question
The height of a cylinder is 4 millimeters. The circumference of its base is \( 10 \pi \mathrm{~mm} \) What is the radius: What is the volume to the nearest tenth:
Ask by Colon Long. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The radius is 5 mm, and the volume is approximately 314.2 mm³.
Solution
The circumference of a circle is given by the formula C = 2πr. Since the circumference is 10π mm:
2πr = 10π
Divide both sides by 2π:
r = (10π) / (2π) = 5 mm
Now, the volume V of a cylinder is given by:
V = πr²h
Substitute r = 5 mm and h = 4 mm:
V = π * (5 mm)² * 4 mm = π * 25 * 4 = 100π mm³
To approximate 100π, take π ≈ 3.14159:
V ≈ 100 * 3.14159 = 314.159 mm³
Rounded to the nearest tenth, the volume is 314.2 mm³.
Summary:
• Radius = 5 mm
• Volume ≈ 314.2 mm³
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
To find the radius of the cylinder, we use the circumference formula: \( C = 2\pi r \). Given that the circumference is \( 10\pi \mathrm{~mm} \), we can set up the equation \( 2\pi r = 10\pi \). Dividing both sides by \( 2\pi \), we find that \( r = 5 \mathrm{~mm} \). Now, to calculate the volume of the cylinder, we can use the formula \( V = \pi r^2 h \). Plugging in our values \( r = 5 \mathrm{~mm} \) and \( h = 4 \mathrm{~mm} \), we get \( V = \pi (5^2)(4) = \pi (25)(4) = 100\pi \mathrm{~mm}^3 \). To the nearest tenth, the volume is approximately \( 314.2 \mathrm{~mm}^3 \).
