Question

Volume of a cone is 1212 cm and its height is 24cm. Find the surface area of the cone.
(14-22)
Find the​

Answer 1

Volume of Cone = $\rm{\mathrm{\pi r}^{2} \dfrac{\mathrm{h}}{3}$

⇒ Volume of Cone = $\rm{\dfrac{\mathrm{\pi r}^{2} \mathrm{h}}{3}$

⇒ 1212 = $\rm{\dfrac{\mathrm{\pi r}^{2} \mathrm{h}}{3}$

⇒ 1212 = $\rm{\dfrac{\mathrm{\dfrac{22}{7}r^2}\mathrm{h}}{3}$  

⇒ 1212 = $\rm{\dfrac{\mathrm{\dfrac{22}{7}r^2}\mathrm{h}}{3}$

⇒ 1212 = $\rm{\dfrac{\mathrm{\dfrac{22}{7}r^2}\mathrm{h}}{3}$  

⇒ 1212 = $\rm{\dfrac{\mathrm{\dfrac{22}{7}r^2}\mathrm{24}}{3}$

⇒ 1212 = $\rm{\mathrm{\dfrac{22}{7}r^2}\mathrm{8}}$

⇒ 1212 = $\rm{\mathrm{\dfrac{176}{7}r^2}}$

⇒ r = 34 cm

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Surface Area of Cone  

$\rm{=\pi r\left(r+\sqrt{h^{2}+r^{2}}\right)}$

$\begin{array}{l}=\dfrac{22}{7} \times 34(34+\sqrt{1157+576}) \\\\=\dfrac{22}{7} \times 34(34+41.62)\end{array}$

=8081.41 cm²