Interactive Quiz: Calculate Volume of Cylinders (V = πr²h).

📚 Quick Study Guide

🔢 Definition: A cylinder is a 3D geometric shape with two parallel circular bases connected by a curved surface. 📐 Key Variables:
• 📏 $r$ = radius of the circular base
• ⬆️ $h$ = height of the cylinder (the perpendicular distance between the bases)
🧮 Formula for Volume: The volume ($V$) of a cylinder is calculated using the formula: $V = \pi r^2 h$, where $\pi$ (pi) is approximately 3.14159. 📐 Units: Ensure that the radius and height are in the same units. The volume will then be in cubic units (e.g., cm³, m³). 💡 Tips:
• 🔍 Double-check your units!
• 📝 Remember to square the radius ($r^2$).
• ✏️ Use a calculator for accurate calculations, especially with $\pi$.

🧪 Practice Quiz

1. What is the volume of a cylinder with a radius of 5 cm and a height of 10 cm?
1. A) 785.4 cm³
2. B) 314.2 cm³
3. C) 1570.8 cm³
4. D) 500 cm³
2. A cylinder has a radius of 3 meters and a height of 7 meters. Calculate its volume.
1. A) 197.92 m³
2. B) 66 m³
3. C) 263.89 m³
4. D) 99 m³
3. If a cylinder has a volume of 471.24 cm³ and a height of 6 cm, what is its radius?
1. A) 4 cm
2. B) 5 cm
3. C) 6 cm
4. D) 7 cm
4. What is the volume of a cylinder with a diameter of 8 inches and a height of 12 inches?
1. A) 603.19 in³
2. B) 2412.74 in³
3. C) 301.59 in³
4. D) 1206.37 in³
5. A cylindrical tank has a radius of 2 meters and a height of 5 meters. How much liquid can it hold?
1. A) 62.83 m³
2. B) 31.42 m³
3. C) 125.66 m³
4. D) 25.13 m³
6. Calculate the volume of a cylinder with a radius of 6 cm and a height of 4 cm.
1. A) 452.39 cm³
2. B) 150.79 cm³
3. C) 301.59 cm³
4. D) 603.19 cm³
7. A cylinder has a volume of 100 cm³ and a radius of 2 cm. What is its height?
1. A) 6.96 cm
2. B) 7.96 cm
3. C) 8.96 cm
4. D) 5.96 cm