Question

a conical tent of capacity 1232m^3 stands on a circular base of area 154m^2.Find in m^2 the area of the canvas​

Answer 1

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Answer 2

$\huge{\mathcal{\underline{\green{SOLUTION }}}}$

Let r = Radius of the base of the conical tent

h = Height of the conical tent

l = Slant Height of the conical tent

So

$Area \: of \: the \: base \: = \pi {r}^{2} \: \: \: {cm}^{2}$

$Volume \: of \: the \: cone \: = \frac{1}{3} \pi{r}^{2} h \: \: {cm}^{3}$

Therefore

$\pi{r}^{2} \: \: = \: 154$

${r}^{2} = 154 \times \frac{7}{22}$

${r}^{2} = \: 49$

$r \: = \sqrt{49} = 7$

Again

$\frac{1}{3} \pi{r}^{2} h \: = 1232$

$Since\: \: \pi{r}^{2} \: \: = \: 154$

So

$\frac{1}{3} \times 154 \times h \: = 1232$

$\implies \: h \: = 1232 \times \frac{3}{154}$

$\implies \: h \: = 24$

Again

${l}^{2} = {r}^{2} + {h}^{2}$

$\implies \: {l}^{2} = {7}^{2} + {24}^{2}$

$\implies \: {l}^{2} = 625$

$\implies \: {l} = \sqrt{625} = 25$

$Hence\: the \: area \: canvas$

$= \pi \: r \: l \: \: \: \: {cm}^{2}$

$= \frac{22}{7} \times 7 \times 25 \: \: {cm}^{2}$

$= 550 \: \: {cm}^{2}$