Question

A 5m wide cloth is used to make a conical tent of Base diameter 14m and height 24m find the cost of the cloth used at the rate of Rs 25per meter

Answer 1

$\large{\underline{\bf{\red{Given:-}}}}$

• ✦ Radius (r) = 14/2 = 7m

• ✦ Height (h) = 24m

$\large{\underline{\bf{\red{To\:Find:-}}}}$

✦ cost of the cloth used at the rate of Rs 25/m

$\huge{\underline{\bf{\purple{Solution:-}}}}$

$\blue{ \bf\:slant \: height \: of \: tent \: (l) = \sqrt{ {r}^{2} + {h}^{2} } }\:$

$\mapsto \rm\: \sqrt{ {7}^{2} + {24}^{2} } \\ \\ \mapsto \rm\: \sqrt{49 + 576} \\ \\\mapsto \rm\: \sqrt{625} \\ \\\mapsto \bf\:25m \\\\ \:$

$\mapsto \blue{ \bf\:CSA \: of \: cone \: = \pi \: rl}$

$\mapsto \rm \frac{22}{7} \times 7 \times 25 \\ \\\mapsto \rm22 \times 25 \\ \\\mapsto \bf550 {m}^{2}$

Let x meter cloth is required:-

$\mapsto \rm \pink{\:CSA \: of \: tent=area \: of \: cloth} \\ \\ \mapsto \rm\:5x = 550 \\ \\ \mapsto \rm\:x = \frac{550}{5} \\ \\\mapsto \bf \pink{\:x = 110}$

So,

110 m cloth is required.

$\mapsto \rm\:Cost \: of \: cloth=\:25 \times 110 \\ \\\mapsto \rm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2750 \\ \\ \mapsto \bf \green{\:Cost \: of \: cloth=2750}$

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Answer 2

$\huge\purple{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\sf{Cost \ of \ cloth \ used \ is \ Rs \ 2750}$

$\sf\ornge{Given:}$

$\sf{For \ cloth,}$

$\sf{\implies{Breadth (b)=5 \ m}}$

$\sf{\implies{Cost \ of \ cloth =Rs \ 25 \ per \ metre}}</p><p>[tex]\sf{For \ cone,}$

$\sf{\implies{Diameter (d)=14 \ m}}$

$\sf{\implies{Height (h)=24 \ m}}$

$\sf\pink{To \ find:}$

$\sf{Cost \ of \ cloth \ used.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{For \ cone,}$

$\sf{Radius(r)=\frac{Diameter (d)}{2}}$

$\sf{Radius(r)=\frac{14}{2}}$

$\sf{Radius (r)=7 \ cm}$

$\sf{Slant \ height (l)=\sqrt{r^{2}+h^{2}}}$

$\sf{...formula}$

$\sf{\therefore{l=\sqrt{7^{2}+24^{2}}}}$

$\sf{l=\sqrt{49+576}}$

$\sf{l=\sqrt{625}}$

$\sf{l=25 \ cm}$

$\sf{Curved \ surface \ area=\pi\times \ r \ h}$

$\sf{...formula}$

$\sf{Curved \ surface \ area=\frac{22}{7}\times7\times25}$

$\sf{\therefore{Curved \ surface \ area=550 \ m^{2}}}$

$\sf{\therefore{550 \ m^{2} \ of \ cloth \ is \ required}}$

__________________________________

$\sf{Area \ of \ cloth \ required=length\times \ breadth}$

$\sf{...formula}$

$\sf{550=Length\times5}$

$\sf{Length=\frac{550}{5}}$

$\sf{\therefore{Length=110 \ m}}$

$\sf{Cost \ of \ cloth \ per \ metre=Rs \ 25}$

$\sf{\therefore{Cost \ of \ 110 \ metre \ of \ cloth}}$

$\sf{=110\times25}$

$\sf{=Rs \ 2750}$

$\sf\purple{\tt{\therefore{Cost \ of \ cloth \ used \ is \ Rs \ 2750}}}$