Math Labs with Activity - Volume of a Right-Circular Cylinder Formula

Math Labs with Activity – Volume of a Right-Circular Cylinder Formula

OBJECTIVE

To demonstrate a method to derive a formula for finding the volume of a right-circular cylinder

Materials Required

1. A right-circular cylinder made of plastic clay (Plasticine)
2. A knife
3. A ruler

Theory
The volume of a right-circular cylinder of height h and base radius r is given by πr²h.

Procedure
Step 1: Take a right-circular cylinder made of plastic clay having height h and base radius r.
Step 2: Cut the cylinder with a sharp knife into eight parts as shown in Figure 37.1.

Step 3: Place the eight parts adjacent to each other to form a solid structure approximately resembling a cuboid as shown in Figure 37.2.

Observations and Calculations
The eight parts together approximately form a cuboid having length πr, breadth r and height h.
∴ the volume of the cuboidal block = πr x r x h = πr²h.
Hence, the volume of the cylinder = πr²h.

Result
The volume of a right-circular cylinder of height h and base radius r is given by πr²h.

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