A hemisphere and cylinder of equal radii have equal total surface areas. Find the ratio of cylinder height to radius.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 1:2.
Total surface area of hemisphere = 3πr2
Total surface area of cylinder = 2πr(h + r)
3πr2 = 2πr(h + r)
⇒ 3πr2 = 2πrh + 2πr2
⇒ 3r = 2h + 2r
⇒ r = 2h
⇒ h/r = 1/2
⇒ h : r = 1 : 2