Question

The radii if the circular ends of a bucket of height $24cm$ are $15cm$and $5cm$. Find the area of its curved surface.

Answer 1

Step 1. Given information

Radius of the top of the bucket$\Rightarrow R=15cm$, radius of the bottom of the bucket$\Rightarrow r=5cm$ and height of the bucket$\Rightarrow H=24cm$.

and $\mathrm{\pi }=3.14$

Formula of Curved Surface Area : $\mathrm{\pi }\times \mathrm{l}\times (\mathrm{R}+\mathrm{r})$

Step 2. Calculation of Slant Height

Formula of Slant height $l=\sqrt{H^2+{(R-r)}^2}$

Hence,

$$\begin{gathered} l=\sqrt{{24}^2+{(15-5)}^2} \\ l=\sqrt{576+{10}^2} \\ l=\sqrt{576+100} \\ l=\sqrt{676} \\ l=26cm \end{gathered}$$

Step 3. Calculation of Curved Surface Area

$$\begin{gathered} \mathrm{\pi }\times \mathrm{l}\times (\mathrm{R}+\mathrm{r}) \\ =\mathrm{\pi }\times 26\times (15+5) \\ =520\mathrm{\pi } \\ =1634.28{\mathrm{cm}}^2 \end{gathered}$$