Test yourself: Grade 8 cone and cylinder volume questions

📚 Quick Study Guide

• 📐 Cone Volume: The volume of a cone is given by the formula $V = \frac{1}{3}\pi r^2 h$, where $r$ is the radius of the base and $h$ is the height.
• 🔢 Cylinder Volume: The volume of a cylinder is given by the formula $V = \pi r^2 h$, where $r$ is the radius of the base and $h$ is the height.
• 🔄 Relationship: Notice that the volume of a cone is exactly one-third the volume of a cylinder with the same base radius and height.
• 📏 Units: Always remember to express your answer in cubic units (e.g., $cm^3$, $m^3$).
• 💡 Tips: Make sure that you are using the same units for both radius and height before doing the calculations.

🤔 Practice Quiz

1. What is the volume of a cone with a radius of 3 cm and a height of 7 cm?
   1. 22 $cm^3$
   2. 66 $cm^3$
   3. 198 $cm^3$
   4. 231 $cm^3$
2. A cylinder has a radius of 5 cm and a height of 10 cm. What is its volume?
   1. 785 $cm^3$
   2. 314 $cm^3$
   3. 1570 $cm^3$
   4. 500 $cm^3$
3. A cone and a cylinder have the same radius and height. If the cylinder's volume is 90 $cm^3$, what is the cone's volume?
   1. 180 $cm^3$
   2. 30 $cm^3$
   3. 90 $cm^3$
   4. 270 $cm^3$
4. What is the height of a cylinder with a volume of 314 $cm^3$ and a radius of 2 cm?
   1. 10 cm
   2. 25 cm
   3. 50 cm
   4. 79 cm
5. A cone has a volume of 100 $cm^3$ and a height of 12 cm. What is its radius (approximately)?
   1. 2.82 cm
   2. 5 cm
   3. 8.86 cm
   4. 15.9 cm
6. The volume of a cylinder is 452 $cm^3$. If the radius is 4 cm, find the height.
   1. 9 cm
   2. 36 cm
   3. 3 cm
   4. 90 cm
7. A cone has a radius of 6 cm and a volume of 301 $cm^3$. Find its height.
   1. 24 cm
   2. 8 cm
   3. 27 cm
   4. 4 cm