a) 3 : 1
b) 13 : 9
c) 17 : 9
d) 34 : 9
Answer: c
Explanation: Let their radius and height be 5x and 12x respectively
Slant height of the cone,
$$l = \sqrt {{{\left( {5x} \right)}^2} + {{\left( {12x} \right)}^2}} = 13x$$
$$\eqalign{
& \frac{{{\text{Total surface area of cylinder}}}}{{{\text{Total surface area of cone}}}} \cr
& = \frac{{2\pi r\left( {h + r} \right)}}{{\pi r\left( {l + r} \right)}} \cr
& = \frac{{2\left( {h + r} \right)}}{{\left( {l + r} \right)}} \cr
& = \frac{{2 \times \left( {12x + 5x} \right)}}{{\left( {13x + 5x} \right)}} \cr
& = \frac{{34x}}{{18x}} \cr
& = \frac{{17}}{9}\,Or\,17:9 \cr} $$
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