In a right circular cylinder, the ratio of the curved surface to the total surface area is 3:7. Find the ratio of the height of the cylinder to the radius of its base.
Answer & explanation
Correct answer: option 1
Curved surface of cylinder = 2\(\pi \)rh
Total surface area of cylinder = (2\(\pi \)rh + 2\(\pi \)r2
According to the question,
⇒ \(\frac{CSA}{TSA}\) = \(\frac{3}{7}\)
⇒ \(\frac{h}{h + r}\) = \(\frac{3}{7}\)
⇒ 7h = 3h + 3r
⇒ 7h - 4h = 3r
⇒ 4h = 3r
⇒ \(\frac{h}{r}\) = \(\frac{3}{4}\)
⇒ h : r = 3 : 4
Therefore, the ratio of height and radius is 3 : 4.