Question

If the radii of the circular ends of a conical bucket which is $45cm$ high be $28cm$ and $7cm$, find the capacity of the bucket.

Answer 1

Step 1: Given information

Height of the conical bucket$=45cm$

The radii of the two circular ends of the conical bucket are $28cm,7cm$

$$\begin{gathered} r_1=28cm \\ {r}_2=7cm \end{gathered}$$

Step 2: Find the volume of the conical bucket

The volume of the conical bucket

$$\begin{gathered} =\frac{1}{3}\mathrm{\pi }({{\mathrm{r}}_1}^2+{{\mathrm{r}}_2}^2+{\mathrm{r}}_1{\mathrm{r}}_2)\mathrm{h} \\ =\frac{1}{3}\mathrm{\pi }\left[{\left(28\right)}^2+{\left(7\right)}^2+28\times 7\right]45 \\ =\frac{1}{3}\mathrm{\pi }(784+49+196)\times 45 \\ =\frac{1}{3}\mathrm{\pi }\times 1029\times 45 \\ =\frac{1}{3}\mathrm{\pi }\times 46305 \\ =15435\times 3.142 \\ =48510{\mathrm{cm}}^3 \end{gathered}$$

Hence, the capacity of the bucket is $48510c{m}^3$