**Math Labs with Activity – Curved Surface Area of a Right-Circular Cone Formula**

**OBJECTIVE**

To demonstrate a method to derive a formula for finding the curved surface area of a right-circular cone (Method 2)

**Materials Required**

- A model of a right-circular cone made of chart paper
- A pair of scissors
- A sheet of white paper

**Theory**

When a cone of slant height l and base radius r made of chart paper (as shown in Figure 34.1) is unfolded, we get a sector of a circular sheet of radius l formed by an arc of length 2πr (as shown in Figure 34.2).

**Procedure**

**Step 1:** Take a right-circular cone having slant height l and base radius r as shown in Figure 34.3.

**Step 2:** Mark a point P on the circular edge of the cone. Mark the vertex of the cone as O. Join OP. Cut the cone along the line OP to get a sector of a circle of radius l formed by an arc of length 2πr.

**Step 3:** Draw three lines in this sector dividing it into four equal sectors as shown in Figure 34.4.

Cut these four sectors and place them adjacent to each other to form a geometrical shape closely resembling a parallelogram as shown in Figure 34.5.

**Observations and Calculations**

The curved surface area of the cone must be equal to the area of the parallelogram formed.

The approximate area of the parallelogram = base x height = πrl.

**Result**

The curved surface area of a right-circular cone having slant height l and base radius r is given by πrl.

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