Question

A conical tent is to be accomodate 22 person each person must have 5m² of space on the ground and 30m³ of air to breadth find the height of conical tent
and explain why ​

Answer 1

Appropriate Question :-

A conical tent is to be accomodate 22 person. Each person must have 5m² of space on the ground and 30m³ of air to breathe. Find the height of conical tent.

$\large\underline{\sf{Solution-}}$

Let assume that radius of base of conical tent is r m and height of conical tent be h m.

Given that,

A conical tent is to be accomodate 22 person, each person must have 5m² of space on the ground.

So, Area of base = 22 × 5 = 110 m²

$\rm\implies \:\pi \: {r}^{2} \: = \: 110 - - - (1)$

Further given that, A conical tent is to be accomodate 22 person, each person 30m³ of air to breathe.

So, Volume of air in conical tent = 22 × 30 = 660 m³

$\rm \: \dfrac{1}{3} \pi {r}^{2}h \: = \: 660$

Now, using equation (1), we get

$\rm \: \dfrac{1}{3} \times 110 \times h \: = \: 660$

$\rm\implies \:h \: = \: 18 \: m$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{CSA_{(cylinder)} = 2\pi \: rh}\\ \\ \bigstar \: \bf{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bf{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bf{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar \: \bf{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bf{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bf{Volume_{(cube)} = {(side)}^{3} }\\ \\ \bigstar \: \bf{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bf{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\ \bigstar \: \bf{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bf{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bf{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$