Question

The height of a cone is$15cm$ and its volume is$1570c{m}^3$. Find the radius of the base. (Use$\pi =3.14$)

Answer 1

Given : Volume $=1570{\mathrm{cm}}^3$ and height $\mathrm{h}=15\mathrm{cm}$

Let radius of the cone be $\mathrm{r}$

We know that Volume of cone$=\frac{1}{3}\mathrm{\pi r}²\mathrm{h}$

According to question,

$$\begin{gathered} \frac{1}{3}\mathrm{\pi r}²\mathrm{h}=1570 \\ \Rightarrow \mathrm{r}²=\frac{(1570\times 3)}{\mathrm{\pi h}} \\ \Rightarrow \mathrm{r}²=\frac{(1570\times 3)}{(3.14\times 15)} \\ \Rightarrow \mathrm{r}²=100 \\ \Rightarrow \mathrm{r}=\surd 100 \\ \Rightarrow \mathrm{r}=10\mathrm{cm} \end{gathered}$$

Hence, Radius of the base$10\mathrm{cm}$.