Math Labs with Activity – Volume of a Right-Circular Cone Formula
To demonstrate a method to derive a formula for finding the volume of a right-circular cone.
- A hollow right-circular cone of known height and base radius
- A hollow cylinder with open top having the same height and base radius as those of the cone
- A few packs of table salt
Step 1: Take a hollow right-circular cone of a known height h and base radius r. Also, take a hollow right-circular cylinder of the same height h and base radius r such that it is open at the top and closed at the bottom.
Step 2: Fill the cone with salt up to the brim, as shown in Figure 40.2.
Pour the entire quantity of salt from the cylinder. Fill the cone again with salt. Pour this salt again into the cylinder. Once again fill the cone with salt and then pour the salt into the cylinder (see Figure 40.3).
Observations and Calculations
We observe that the volume of a cylinder is three times the volume of a cone of the same height h and the same base radius r. Since the volume of a cylinder with height h and base radius r is given by πr²h, therefore the volume of a cone with height h and base radius r will be 1/3 πr²h.
The volume of a right-circular cone of the height h and base radius r is given by 1/3 πr²h.