**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**

- A right-circular cylinder made of plastic clay (Plasticine)
- A knife
- 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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