Question : If the curved surface area of a solid cylinder is two-fifths of its total surface area, then what is the ratio of its diameter to its height?
Option 1: 2 : 5
Option 2: 1 : 2
Option 3: 2 : 3
Option 4: 3 : 1
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Correct Answer: 3 : 1
Solution : As we know, Curved surface area of cylinder = $2 \pi rh$ Total surface area of cylinder = $2 \pi r(h + r)$ where $r$ is the radius and $h$ is the height of the solid cylinder Diameter, $d$ = $2r$ According to the question $\frac{2 \pi rh}{2 \pi r (r + h)]} = \frac{2}{5}$ ⇒ $\frac{h}{r+h}=\frac25$ ⇒ $5h=2r+2h$ ⇒ $3h=d$ ⇒ $\frac{d}{h}=\frac31$ Hence, the correct answer is 3 : 1.
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