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Question:

Note Use $\pi=\frac{22}{7}$, unless stated otherwise.

A conical tent is $10 \mathrm{~m}$ high and the radius of its base is $24 \mathrm{~m}$. Find the slant height of the tent. If the cost of $1 \mathrm{~m}^{2}$ canvas is $₹ 70$, find the cost of canvas required to make the tent.

 

Solution:

Radius of the conical tent, r = 24 m

Height of the conical tent, h = 10 m

$\therefore$ Slant height of the conical tent, $l=\sqrt{r^{2}+h^{2}}=\sqrt{24^{2}+10^{2}}=\sqrt{576+100}=\sqrt{676}=26 \mathrm{~m}$

Curved surface area of the conical tent $=\pi r l=\frac{22}{7} \times 24 \times 26 \mathrm{~m}^{2}$

The cost of 1 m2 canvas is ₹ 70.

∴ Cost of canvas required to make the tent

= Curved surface area of the conical tent × ₹ 70

$=\frac{22}{7} \times 24 \times 26 \times 70$

= ₹ 1,37,280

Thus, the cost of canvas required to make the tent is ₹ 1,37,280.

 

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