Question

A joker’s cap is in the form of a right circular cone of base radius $7cm$ and height $24cm$. Find the area of the sheet required to make $10$ such caps. (Assume $\mathrm{\pi }=\frac{22}{7}$)

Answer 1

Step 1: Find the slant height of the conical cap

Curved surface area of cone is $\mathrm{\pi rl}$.

Since, Radius of conical cap ($r$) $=7cm$

Height of conical cap ($h$) $=24cm$

Area of the sheet required to make $1$cap$=\mathrm{\pi rl}$ (where $l$ is the slant height and $l=\sqrt{r^2+h^2}$)

Now,

$$\begin{gathered} \Rightarrow l=\sqrt{7^2+{24}^2} \\ \Rightarrow l=\sqrt{49+576} \\ \Rightarrow l=\sqrt{625} \\ \Rightarrow l=25 \end{gathered}$$

Step 2: Find the area of sheet require to make $10$ such caps

Area of the sheet required to make $1$cap $=\mathrm{\pi rl}$

$$\begin{gathered} =\frac{22}{7}\times 7\times 25 \\ =22\times 25 \\ =550c{m}^2 \end{gathered}$$

So, area of the sheet required to make $10$ such caps$=10\times 550=5500c{m}^2$

Hence, area of the required sheet is $5500c{m}^2$