Volume of cylinders cones spheres test

📚 Quick Study Guide

• 📐 Cylinder Volume: Volume is the area of the base times the height. For a cylinder, the base is a circle, so the volume is $V = \pi r^2 h$, where $r$ is the radius and $h$ is the height.
• 🍦 Cone Volume: A cone's volume is one-third the volume of a cylinder with the same base and height: $V = \frac{1}{3} \pi r^2 h$.
• 🏀 Sphere Volume: The volume of a sphere depends only on its radius: $V = \frac{4}{3} \pi r^3$.
• 💡 Key Tip: Make sure your units are consistent (e.g., all in cm or all in meters) before calculating!
• 📝 Remember: $\pi$ (pi) is approximately 3.14159.

Practice Quiz

1. What is the volume of a cylinder with a radius of 5 cm and a height of 10 cm?
   1. 785.4 $cm^3$
   2. 314.2 $cm^3$
   3. 1570.8 $cm^3$
   4. 500 $cm^3$
2. A cone has a radius of 3 cm and a height of 6 cm. What is its volume?
   1. 56.55 $cm^3$
   2. 169.65 $cm^3$
   3. 339.29 $cm^3$
   4. 113.10 $cm^3$
3. What is the volume of a sphere with a radius of 4 cm?
   1. 64 $cm^3$
   2. 201.06 $cm^3$
   3. 268.08 $cm^3$
   4. 804.25 $cm^3$
4. A cylinder and a cone have the same radius and height. If the cylinder's volume is 90 $cm^3$, what is the cone's volume?
   1. 30 $cm^3$
   2. 45 $cm^3$
   3. 90 $cm^3$
   4. 270 $cm^3$
5. A sphere has a diameter of 10 cm. What is its volume?
   1. 523.6 $cm^3$
   2. 4188.8 $cm^3$
   3. 104.72 $cm^3$
   4. 314.16 $cm^3$
6. What is the height of a cylinder with a volume of 628 $cm^3$ and a radius of 4 cm?
   1. 12.5 cm
   2. 25 cm
   3. 50 cm
   4. 6.25 cm
7. A cone has a volume of 100 $cm^3$ and a height of 12 cm. What is the radius of the cone's base?
   1. 2.82 cm
   2. 5.13 cm
   3. 8.92 cm
   4. 1.67 cm