Question

in circus a tent of height 18m and radius 6m is laid what its slant height find the cost of canvas cloth required for tent if it is cost rs 10per sqm​

Answer 1

⠀⠀⠀⠀⠀⠀⠀$\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(18,1.6){\sf{6m}}\put(9.5,10){\sf{18m}}\end{picture}$

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• As it is given in the question that the tent is in the shape of cone.

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Given

• Height of the conical tent is 18m.
• Radius of the conical tent is 6m.
• Cost of canvas cloth = Rs10 per meter.

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To find

• Slant height of the conical tent.
• Cost of canvas cloth required for the tent.

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Solution

• Let us firstly find the slant height of the given tent.

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{We\: know\: that}}}$

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$\large\bf{\underline{\boxed{l = \sqrt{r^2 + h^2}}}}$

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Here,

⠀⠀⠀⠀⠀❍ l = slant height

⠀⠀⠀⠀⠀❍ r = radius

⠀⠀⠀⠀⠀❍ h = height

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$\tt\longrightarrow{l = \sqrt{(6)^2 + (18)^2}}$

$\tt\longrightarrow{l = \sqrt{36 + 324}}$

$\tt\longrightarrow{l = \sqrt{360}}$

$\tt\longrightarrow{l = 6\sqrt{10}}$

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• Now, point to be noted here that the cloth needed to cover the tent actually means the curved surface area of the tent.

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{Using\: the\: Formula}}}$

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$\large\bf{\underline{\boxed{CSA_{(Cone)} = \pi rl}}}$

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• Putting the values

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$\tt:\implies\: \: \: \: \: \: \: \: {CSA = \dfrac{22}{7} \times 6 \times 6\sqrt{10}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {CSA = \dfrac{22 \times 6}{7} \times 6\sqrt{10}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {CSA = \dfrac{132}{7} \times 6\sqrt{10}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {CSA = 18.85 \times 6\sqrt10}$

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• Here, we use

$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{6\sqrt{10} = 18.97}}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {CSA = 18.85 \times 18.97}$

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$\bf:\implies\: \: \: \: \: \: \: \: {CSA = 357.58}$

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• We get CSA of the tent is 357.58 m².

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{Finding\: the\: total\: cost}}}$

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$\tt\longmapsto{Cost = Rs(357.58 \times 10)}$

$\tt\longmapsto{Cost = Rs3,575.8}$

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Hence,

• The total cost of the canvas cloth required to cover the tent is Rs3,575.8 .

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Answer 2

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$\boxed{\underline{\bold{This\:sum\:is\:from\:chapter\:-\:Suraface\:area\:(SA)\:and\:volume}}}$

$\underline {\underline {\bf {Given}}}\begin{cases} & \sf{\bullet\:\:Circus\:tent\:of\;height\;\bf{18\;m}} \\ & \sf{\bullet\:\:Base\:radius\;of\;circus\;tent\:is\:\bf{6\;m}} \end{cases}$

$\underline {\underline {\bf {To\:Find}}}\begin{cases} & \sf{\bullet\:\:Slant\:height\:of\:the\:circus\:tent?} \\ & \sf{\bullet\:\:Cost \:of \:canvas \:cloth\: required \:for \:tent\:,\:if\: it's\: cost\:is\: Rs.\:10\:per \:sq.m!} \end{cases}$

${ \bold{ \underline { \underline {Diagram :}}}} \:$

$\underline {\bf {Here,}}\begin{cases} & \sf{\bullet\:\:Height\:(h)\:=\:\bold{18\:m}} \\ & \sf{\bullet\:\:Slant \:height\: (l)\:= \:\bf{?}} \\ & \sf{\bullet\:\:Radius\:(r)\:=\: \bf{6\:m}} \end{cases}$

$\qquad\qquad$ $\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(18,1.6){\sf{6\;m}}\put(9.5,10){\sf{18\;m}}\end{picture}$

• Dear user, if you are not able to see the diagram from app. Please see it from the the site (Brainly.in). It will be correctly displayed there.

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$\qquad\qquad\large\underbrace{\underline{\sf{How\:to\:solve\:it\::}}}$

Here, we are given height and radius of circus tent, we had to find out it's slant height. We will find out it by using formula l² = r² + h². Then, the question say's to us to find cost of canvas cloth required for tent if it cost Rs. 10 per sq.m. To find cost, firstly we will find it's curved surface area (C.S.A) of cone , it's formula is πrl. Then, we will multiply it's C.S.A with cost of canvas per sq.m to get our answer!

$\qquad\large\underbrace{\underline{\sf{So,\:let's\:start\:solving\:it\::}}}$

${ \bold { \underline {Solution :}}} \:$

$\qquad \small{\rm{ \underline {\bigstar\:Formula\:that\:we\:will\:use\:to\:find\:slant\:height :-}}} \:$

$\boxed{\boxed{\underline{\overline {\sf {\mid\:l^2\:=\:r^2 \: + \: h^2\:\mid}}}}}$

$\underline {\bf {Here,}}\begin{cases} & \sf{\bullet\:\:h\:=\:\bold{height}} \\ & \sf{\bullet\:\: l\:= \:\bf{slant \:height}} \\ & \sf{\bullet\:\:r\:=\: \bf{radius}} \end{cases}$

$\qquad \qquad\tiny \: {\underline{\rm {\bigstar\:Putting\:all\:values\:in\:the\:formula :}}}$

$\qquad\ratio\longmapsto\:\sf{l^2\:=\:(6)^2 \: + \: (18)^2}$

$\qquad\ratio\longmapsto\:\sf{l^2\:=\:36 \: + \: 324}$

$\qquad\ratio\longmapsto\:\sf{l^2\:=\:360}$

$\qquad\ratio\longmapsto\:\sf{l\:=\:\sqrt{360}}$

$\qquad\ratio\longmapsto\:\sf{l\:=\:18.97}$

$\underline{\underline{\boxed {\sf {\therefore {Slant\:height\:of\:circus\:tent\:\approx\:\bold{18.97\:m}}}}}}\:\green\bigstar$

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Now, we have to find it's C.S.A !!

$\qquad \small {\rm{ \underline {\bigstar\:Formula\:that\:we\:will\:use\:to\:find\:it's\:C.S.A :-}}} \:$

$\boxed{\boxed{\underline{\overline {\sf {\mid\:Curved\:surface\:area_{(Circus\:tent)}\:=\:\pi r l\:\mid}}}}}$

$\qquad \qquad\tiny \: {\underline{\rm {\bigstar\:Putting\:all\:values\:in\:the\:formula :}}}$

$\qquad\ratio\implies\:\sf{\dfrac{22}{7}\:\times\:6\:\times\:18.97}$

$\qquad\ratio\implies\:\sf{\dfrac{22\:\times\:6}{7}\:\times\:18.97}$

$\qquad\ratio\implies\:\sf{\dfrac{132}{7}\:\times\:18.97}$

$\qquad\ratio\implies\:\sf{\dfrac{\cancel{132}}{\cancel{7}}\:\times\:18.97}$

$\qquad\ratio\implies\:\sf{18.85\:\times\:18.97}$

$\qquad\ratio\implies\:\sf{357.58}$

$\underline{\underline{\boxed {\sf {\therefore {C.S.A\:of\:cone\:\approx\:\bold{357.58\:m^2}}}}}}\:\red\bigstar$

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Now, finding the cost of canvas cloth :-

$\boxed{\boxed{\underline{\overline {\sf {\mid\:\:Cost\: of \:canvas\: cloth\:=\:C.S.A\: \times \: 10\:\mid}}}}}\dashrightarrow\bold{(1)}$

$\qquad \qquad\tiny \: {\underline{\rm {\bigstar\:Putting\:all\:values\:in\:(1) :}}}$

$\qquad\leadsto\:\sf{357.58\:\times\:10}$

$\qquad\leadsto\:\sf{3575.8}$

$\underline{\underline{\boxed {\sf {\therefore {Cost\:of\:canvas\:required\:for\:it\:\approx\:\bold{Rs.\:3,575.8\:}}}}}}\:\blue\bigstar$

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