Question

A conical tent is $10m$ high and the radius of its base is$24m$. Find slant height of the tent and cost of the canvas required to make the tent, if the cost of $1{m}^{2}$ canvas is $Rs.70$.

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Solution

Step 1 - Finding the slant height of the tent.It is given that, radius of conical tent $=24m$ and height of the conical tent $=10m$Now, by the relation between the slant height, radius and height of the cone${l}^{2}={r}^{2}+{h}^{2}\phantom{\rule{0ex}{0ex}}{l}^{2}={24}^{2}+{10}^{2}\phantom{\rule{0ex}{0ex}}{l}^{2}=576+100\phantom{\rule{0ex}{0ex}}{l}^{2}=676\phantom{\rule{0ex}{0ex}}l=\sqrt{676}\phantom{\rule{0ex}{0ex}}l=26m$Therefore the slant height of the cone is $26m$.Step 2 - Finding the cost of the canvasTo Find the cost of the canvas we need to find the curved surface area of the Cone.Curved surface area of the cone $=\pi rl$ $\phantom{\rule{0ex}{0ex}}=\frac{22}{7}×24×26\phantom{\rule{0ex}{0ex}}=\frac{13728}{7}{\mathrm{m}}^{2}$Cost of $1{m}^{2}$ canvas = $₹70$Therefore, the cost of $\frac{13728}{7}{m}^{2}$ canvas = $\frac{13728}{7}×70=137280$Hence, the cost of canvas of the conical tent $₹137280$.

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