Question

In the marriage ceremony of his son Aman , Ashok has to make arrangements for the accomodation of 150 Persons. For this purpose , he plans to build a conical tent in such a way that each person have 4 sq metres of the space on ground and 20 cubic metres of air to breath . What should be the height of the conical tents ?​

Answer 1

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$\small \red{{Let \: the \: height \: of \: the \: Conical \: tent \: = h \: metre. }}\\\small \red{{Radius \: of \: the \: base \: of \: the \: cone \: = \: r m}}$

$\small \blue{{The \: tent \: has \: to \: accomodate \: 150 \: persons \: }} \\ \small \pink{{The \: space \: required \: by \: each \: person \: on the \: ground }} \\ \small \pink{{ = 4 sq. \: metres .}}$

$\small \green{{And \: Amount \: of \: air \: = 20 \: m^{3}}} \\ \small{\therefore \orange{\ Area \: of \: the \: base = 150 \times 20 = 3000 \: m^{2}}} \\ \rightarrow \small \red{{\pi \:r^{2} = 600 \: m^{2} = \frac{22}{7}r^{2} = 600 \: m^{2} }} \\ \rightarrow\small \pink{{ \: r ^{2} = \frac{600 \times 7}{22} \: m^{2} \rightarrow \: r = 13.817 \: m }}$

$\small \red{ {Volume \: of \: the \: cone \: = 150 \times 20 = 3000 \: m ^{3} }} \\ \small \blue{ \mapsto \: \frac{1}{3} \pi \: r^{2} \: h = 3000 \: m ^{3} \rightarrow \frac{1}{3} \times \frac{22}{7} \times (13.817)^{2} \times h \: = 3000} \\ \mapsto \small \green{{h = \frac{3000 \times 7 \times 3}{22 \times (13.817)^{2} \: \ } }} = 15 \: m$

$\small \red{{Hence , \: height \: of \: the \: conical \: tent \: = 15 \: m.}}$

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