Cone Volume Worksheet Answer Key
Calculating the volume of a cone is a fundamental concept in geometry and mathematics. This worksheet answer key will guide you through the process of finding the volume of different cones.
Understanding the Formula
The volume of a cone is given by the formula:
V = (1⁄3)πr²h
Where: - V is the volume of the cone - π is a mathematical constant approximately equal to 3.14 - r is the radius of the cone’s base - h is the height of the cone
Worksheet Answer Key
Question 1:
Find the volume of a cone with a radius of 4 cm and a height of 6 cm.
📝 Note: Use the formula V = (1/3)πr²h
Solution: V = (1⁄3)π(4)²(6) = (1⁄3) × 3.14 × 16 × 6 = 100.48 cubic cm
Question 2:
A cone has a volume of 150 cubic inches. If the radius of its base is 5 inches, find the height of the cone.
📝 Note: Rearrange the formula to solve for h
Solution: 150 = (1⁄3)π(5)²h 150 = (1⁄3) × 3.14 × 25 × h 150 = 26.17h h = 150 / 26.17 = 5.73 inches
Question 3:
Find the volume of a cone with a radius of 3 m and a height of 8 m.
Solution: V = (1⁄3)π(3)²(8) = (1⁄3) × 3.14 × 9 × 8 = 75.36 cubic meters
Question 4:
A cone has a volume of 300 cubic feet. If the height of the cone is 10 feet, find the radius of its base.
📝 Note: Rearrange the formula to solve for r
Solution: 300 = (1⁄3)π®²(10) 300 = (1⁄3) × 3.14 × r² × 10 300 = 10.47r² r² = 300 / 10.47 = 28.65 r = √28.65 = 5.35 feet
| Question | Radius (r) | Height (h) | Volume (V) |
|---|---|---|---|
| 1 | 4 cm | 6 cm | 100.48 cubic cm |
| 2 | 5 inches | 5.73 inches | 150 cubic inches |
| 3 | 3 m | 8 m | 75.36 cubic meters |
| 4 | 5.35 feet | 10 feet | 300 cubic feet |
To summarize, finding the volume of a cone involves using the formula V = (1⁄3)πr²h. By understanding this formula and rearranging it to solve for different variables, you can find the volume, radius, or height of a cone.
What is the formula for the volume of a cone?
+The formula for the volume of a cone is V = (1⁄3)πr²h.
How do I find the height of a cone if I know its volume and radius?
+Rearrange the formula to solve for h: h = (3V) / (πr²).
What is the unit of measurement for the volume of a cone?
+The unit of measurement for the volume of a cone is cubic units (e.g., cubic centimeters, cubic inches, cubic meters, etc.).
Related Terms:
- Volume of cones Questions
- Volume of a cone worksheet
- Volume of Cone Worksheet Kuta
