Question

The radii of the ends of a bucket 30 cm high are 21 cm and 7 cm. Find its capacity in litres and the amount of sheet required to make this bucket.

Answer 1

Height of the bucket = 30 cm.

Therefore,

Capacity of the bucket

The slant height of the bucket

$$\begin{gathered} l=\sqrt{h^2+{\left(r_1-r_2\right)}^2} \\ =\sqrt{900+{\left(21-7\right)}^2} \\ =\sqrt{900+196} \\ =\sqrt{1096}=33.105\mathrm{cm} \end{gathered}$$

Total C.S.A. of the bucket

$$\begin{gathered} =\mathrm{\pi }\left({\mathit{r}}_{\mathit{1}}\mathit{+}{\mathit{r}}_{\mathit{2}}\right)\times l \\ \mathit{=}\mathrm{\pi }\left(21+7\right)\times 33.1 \end{gathered}$$
$$\begin{gathered} =88\times 33.1 \\ \approx 2913{\mathrm{cm}}^2 \end{gathered}$$

Area of the base

Total sheet required to make this bucket

$$\begin{gathered} =2913+154 \\ =3067{\mathrm{cm}}^2 \end{gathered}$$