Question

The volume of right circular cone is 9850msq . If the diameter of the base is 25 m . Find the height , slant height and curved surface area of the cone .

Answer 1

Dear student
$$\begin{gathered} Volumeofcone=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h} \\ \mathrm{where}\mathrm{r}\mathrm{is}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{cone}\mathrm{and}\mathrm{h}\mathrm{is}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{cylinder} \\ \mathrm{Given}\mathrm{diameter}=25\mathrm{m} \\ \mathrm{So}\mathrm{radius}=\frac{25}{2}\mathrm{m} \\ \mathrm{Also}\mathrm{volume}=9850 \\ \Rightarrow 9850=\frac{1}{3}\times \frac{22}{7}\times {\left(\frac{25}{2}\right)}^2\times \mathrm{h} \\ \Rightarrow \mathrm{h}=60\mathrm{m}\mathrm{approx} \\ \mathrm{also}\mathrm{slant}\mathrm{height}\mathrm{l}=\sqrt{{\mathrm{h}}^2+{\mathrm{r}}^2} \\ =\sqrt{{60}^2+12.5^2} \\ =61\mathrm{m}\mathrm{approx} \\ \mathrm{Now}\mathrm{CSA}=\mathrm{\pi rl} \\ =\frac{22}{7}\times \frac{25}{2}\times 61 \\ =2396{\mathrm{m}}^2 \end{gathered}$$
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