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Question
A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and height are in the ratio 5 : 12, write the ratio of the total surface area of the cylinder to that of the cone.
Solution
Given that
r : h = 5 :12
i.e. r = 5x , h =12x
Since,
Right, circular cone and right circular cylinder have equal base and equal right.
Therefore,
The total surface area of cylinder `S_1 = 2pir (h + r)`
The total surface area of cone `S_2 = pir(l + r)`
`l = sqrt(r^2 + h^2)`
`= sqrt(25x^2 + 144x^2)`
`=sqrt(169x^2)`
`l = 13x`
Now,
`S_1/S_2 = (2pir(h + r))/(pir (l +r))`
`= (2(h+r))/(l+r)`
`S_1 /S_2 = (2(12x + 5x))/(13x + 5x)`
`=(2xx 17x)/(18x)`
`S_1 /S_2 = 17/9`
Hence,`S_1 : S_2 = 17 : 9`
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