The respective ratio between numerical values of the curved surface area and the volume of a right circular cylinder is 2 : 3. If the respective ratio between the radius and the height of the cylinder is 3 : 7, what is the total surface area of the cylinder?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 60π cm2.
Given that
The ratio of the curved surface area and the volume of a right circular cylinder = 2 : 3
The ratio of the radius and the height of the cylinder = 3 : 7
A cylinder's volume is π r² h, and its curved surface area is 2π r h
Total surface area of the cylinder = 2π r (h + r)
where r is the radius and h is the height of the cylinder
r/h = 3/7
⇒ 2πrh /πr2h = 2/3
⇒ 2/r = 2/3
⇒ r = 3 cm
h = 7 cm
Hence. the total surface area of the cylinder = 2π × 3 (7 + 3) = 60π cm2