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Surface Areas and Volumes | Surface Areas and Volumes - Exercise 13.3

Question 4

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)

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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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Question 4

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)

Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

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.

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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