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 cloth required to make 10 such caps.

Given, r = 7 cm and h = 24 cm.

We know that,

$l = \sqrt{r^2 + h^2}$

Putting values in the formula we get,

$\Rightarrow l = \sqrt{(7)^2 + (24)^2} \\[1em] \Rightarrow l = \sqrt{49 + 576} \\[1em] \Rightarrow l = \sqrt{625} = 25 \text{ cm}.$

Curved surface area of cone = πrl.

Putting values in equation,

Curved surface area of cap = $\dfrac{22}{7} \times 7 \times 25$ = 22 × 25 = 550 cm².

∴ Curved surface area of 10 caps = 10 × 550 = 5500 cm².

Hence, the area of the cloth required to make 10 such caps is 5500 cm².