Question

the volume of cone is 616 cm3 and height is 21cm find its radius and c.s.a​

Answer 1

$\bold{Given:-} \begin{cases} \sf{ \red{\star \: }V_{Cone}=616 \:{ Cm. }^{3} } \\ \sf{ \red \star \: height = 21 \: Cm.} \\ \sf{ \red \star \: To \: Find:-} \\ \sf{ \red \star \: r = \: ?} \\ \sf{ \red \star \: C.S.A = \: ?} \end{cases}$

$\\ \\ \bold \red\star \: \underline{Solution:-}$

$\: \: \: \: \: { \purple{\large\boxed{V_{Cone} = \frac{1}{3} \pi {r}^{2}h. }}}\\ \\ \implies \: 616 = \frac{1}{3} \times \frac{22}{7} \times {r}^{2} \times 21. \\ \\ \implies \: 616 = \frac{1}{3} \times \frac{22 {r}^{2} }{ \cancel7} \times \cancel {21}. \\ \\ \implies \: 616 = \frac{1}{ \cancel3} \times \cancel{3} \times 22{r}^{2} . \\ \\ \implies \: \frac{ \cancel{616}}{ \cancel{22}} = {r}^{2} . \\ \\ \implies \: 28 = {r}^{2} . \\ \\ \implies \: r = 2 \sqrt{7} \\ \\ .$

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$\bold \red\star \: \underline{For \: Slant \: Height (l)}$

${l}^{2} = {r}^{2} + {h}^{2} . \\ \\ l = \sqrt{ {r}^{2} + {h}^{2} } . \\ \\ \: \: = \sqrt{{( 2\sqrt{7}) }^{2} + {(21 )}^{2} } . \\ \\ \: \: = \sqrt{28 + 441}. \\ \\ \: \: = \sqrt{469} \: Cm.$

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$\bold \red\star \: \underline{Curved \: Surface \: Area \: (C.S.A)}$

$C.S.A = \pi rl \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{22}{ \cancel7} \times 2 \sqrt{ 7} \times \cancel {7.67}. \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: =22 \times 2 \sqrt{7} \times 0.67. \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 77.8272 \: Cm.$

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$\bold \red\star \: \underline{Some \: Information:- }\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red{V_{Cone} = \frac{1}{3} \pi rl.}\\ \\ \red{Slant \: Height = {r}^{2} + {h}^{2} . }\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \red{\sqrt{7} = 2.645751(Approximately.)} }\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red{ \sqrt{469} = 7.67(Approximately.)}$

$\red {\huge {\boxed{keep \: \: smile: )}}}$