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
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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