Solved examples: finding cylinder height or radius

📚 Quick Study Guide

• 📏 The volume $V$ of a cylinder is given by the formula: $V = \pi r^2 h$, where $r$ is the radius and $h$ is the height.
• 📐 The surface area $A$ of a cylinder is given by the formula: $A = 2\pi r^2 + 2\pi r h$.
• 🔄 To find the height $h$ when the volume $V$ and radius $r$ are known: $h = \frac{V}{\pi r^2}$.
• 🔍 To find the radius $r$ when the volume $V$ and height $h$ are known: $r = \sqrt{\frac{V}{\pi h}}$.
• 💡 Remember to use consistent units for all measurements.

Practice Quiz

1. A cylinder has a volume of $500\pi$ cubic cm and a radius of 5 cm. What is its height?
   1. 5 cm
   2. 10 cm
   3. 20 cm
   4. 25 cm
2. A cylinder has a volume of $1000$ cubic inches and a height of 10 inches. What is its radius (approximately)?
   1. 3.16 inches
   2. 5.64 inches
   3. 6.28 inches
   4. 10 inches
3. A cylinder has a volume of $250\pi$ cubic meters and a height of 10 meters. What is the radius?
   1. 2.5 m
   2. 5 m
   3. 7.5 m
   4. 10 m
4. A cylinder has a volume of $72\pi$ cubic feet and a radius of 3 feet. Find the height.
   1. 4 ft
   2. 6 ft
   3. 8 ft
   4. 12 ft
5. A cylinder has a volume of $98\pi$ cubic inches and a height of 2 inches. What is the radius?
   1. 4 in
   2. 7 in
   3. 14 in
   4. 49 in
6. The volume of a cylinder is $196\pi$ cubic cm and the radius is 7 cm. What is the height?
   1. 2 cm
   2. 4 cm
   3. 8 cm
   4. 14 cm
7. A cylinder has a volume of $64\pi$ cubic meters and a height of 4 meters. Calculate the radius.
   1. 2 m
   2. 4 m
   3. 8 m
   4. 16 m