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Question 44

A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and the height are in the ratio 5 : 12, then the ratio of the total surface area of the cylinder to that of the cone is

Solution

Let radius of both be $$r=5$$ and height be $$h=12$$ units

=> Slant height of cone = $$l=\sqrt{(5)^2+(12)^2}=\sqrt{25+144}$$

=> $$l=\sqrt{169}=13$$ units

=> Total surface area of cylinder : Total surface area of cone = $$2\pi r(r+h):\pi r(r+l)$$

= $$2r+2h:r+l$$

= $$\frac{10+24}{5+13}=\frac{34}{18}$$

= $$17:9$$

=> Ans - (C)

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