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9) S.A. of sphere; r = 12 cm, is 5 times the C.S.A. of a cone of radius 11 cm. Find h and v of cone ?

Dear Student,

Please find below the solution to the asked query:

We know :  Surface area of sphere = 4 $\mathrm{\pi }$ r²   and Curved surface area of cone = $\mathrm{\pi }r\sqrt{r^2 +h^2}$  And from given information we get :

$$\begin{gathered} 4 \times \mathrm{\pi } \times {12}^2 = 5 \times \mathrm{\pi } \times 11 \times \sqrt{{11}^2 +h^2} \\ \Rightarrow 4 \times 12 \times 12= 5 \times 11 \times \sqrt{121+h^2} \\ \Rightarrow \sqrt{121+h^2} = \frac{576}{55} \\ \mathrm{Taking} \mathrm{whole} \mathrm{square} \mathrm{on} \mathrm{both} \mathrm{hand} \mathrm{side} : \\ \Rightarrow {\left(\sqrt{121+h^2}\right)}^2 = {\left(\frac{576}{55}\right)}^2 \\ \Rightarrow 121+h^2 = \frac{331776}{3025} \\ \Rightarrow h^2 = \frac{331776}{3025} - 121 \\ \Rightarrow h^2 = \frac{331776 - 366025}{3025} \\ \mathbf{\Rightarrow }{\mathit{h}}^{\mathbf{2}}\mathbf{ }\mathbf{=}\frac{\mathbf{-}\mathbf{34249}}{\mathbf{3025}} \end{gathered}$$
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