A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.

To find the area of the sheet required to make 10 joker’s caps, we first need to calculate the surface area of one cap, which is in the shape of a right circular cone.

Step 1: Calculate the Slant Height

The slant height (l) of a cone can be found using the Pythagorean theorem:

• l = √(r² + h²)

Here, r is the radius (7 cm) and h is the height (24 cm).

Calculating:

• l = √(7² + 24²) = √(49 + 576) = √625 = 25 cm

Step 2: Calculate the Surface Area of One Cap

The surface area (A) of a cone is given by the formula:

• A = πr(l + r)

Substituting the values:

• A = π × 7 × (25 + 7) = π × 7 × 32
• A ≈ 3.14 × 7 × 32 ≈ 703.84 cm²

Step 3: Calculate the Total Area for 10 Caps

Now, to find the total area for 10 caps:

• Total Area = 10 × A = 10 × 703.84 cm² ≈ 7038.4 cm²

Final Result

The area of the sheet required to make 10 joker’s caps is approximately 7038.4 cm².