- Surface Areas and Volumes - Exercise 13.1
- Surface Areas and Volumes - Exercise 13.2
- Surface Areas and Volumes - Exercise 13.3
- Surface Areas and Volumes - Exercise 13.4
- Surface Areas and Volumes - Exercise 13.5
- Surface Areas and Volumes - Exercise 13.6
- Surface Areas and Volumes - Exercise 13.7
- Surface Areas and Volumes - Exercise 13.8
- Surface Areas and Volumes - Exercise 13.9
NCERT Solutions Class 9 Mathematics Solutions for Surface Areas and Volumes - Exercise 13.3 in Chapter 13 - Surface Areas and Volumes
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A conical tent is 10 m high and the radius of its base is 24 m. Find
(i) slant height of the tent.
(ii)cost of the canvas required to make the tent, if the cost of 1 m2 canvas is Rs 70.
(Assume π=22/7)
Let ABC be a conical tent
Height of conical tent, h = 10 m
The radius of a conical tent, r = 24 m
Let the slant height of the tent be l.
(i)In the right triangle, ABO,
\begin{aligned} &\mathrm{AB}^{2}=\mathrm{AO}^{2}+\mathrm{BO}^{2} \text { (using Pythagoras theorem) }\\ &l^{2}=h^{2}+r^{2}\\ &=(10)^{2}+(24)^{2}\\ &=676 \end{aligned}
l = 26
Therefore, the slant height of the tent is 26 m.
(ii) CSA of tent = πrl
\begin{aligned} &=(22 / 7 \times 24 \times 26) \mathrm{m}^{2}\\ &\text { Cost of } 1 \mathrm{m}^{2} \text { canvas }=\mathrm{Rs} 70\\ &\text { cost of }(13728 / 7) \mathrm{m}^{2} \text { canvas is equal to } \mathrm{Rs}(13728 / 7) \times 70=\mathrm{Rs} 137280 \end{aligned}
Therefore, the cost of the canvas required to make such a tent is Rs 137280.
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