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Question

A tent is of the shape of a right circular cylinder upto a height of $$3$$ m and then becomes a right circular cone with a maximum height of $$13.5$$ m above the ground. Calculate the cost of painting the inner side of the tent at the rate of Rs. $$2$$ per sq m, if the radius of the base is $$14$$ m.


Solution


Surface area to be painted = $$\pi rl+2\pi r{ h }^{ 1 }$$
                                              = $$\pi r\left( \sqrt { { r }^{ 2 }+{ h }^{ 2 } } +{ h }^{ 1 } \right) $$
                                              = $$\dfrac { 22 }{ 7 } \times 14\left( \sqrt { { 14 }^{ 2 }+{ 10.5 }^{ 2 } } +3 \right) $$
                                              = 44 $$\times $$ 20.5
                                              = $${ 902m }^{ 2 }$$
Total cost of painting = Rs. $$\left( 902\times 2 \right) $$
                                    = Rs. $$1804$$

946688_563960_ans_8f355988c4da495a821eddac91185561.jpg

Mathematics

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