A cylindrical vessel of height 14 cm has outer and inner radii 14 cm and 10 cm, respectively. It is to be filled by transferring water in it by using a small cylinder height 7 cm and outer and inner radii 7 cm and 5 cm, respectively. What will be unfilled height of the big vessel after transferring water 6 times by using the smaller cylinder? (Use π = 22/7)
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e 3.5 cm.
Volume of water in big vessel (inner cylinder)
Height = 14 cm and Inner radius = 10 cm
Volume = π × r² × h = (22/7) × 10² × 14 = 4400 cm³
Volume of water in small cylinder (inner cylinder)
Height = 7 cm and Inner radius = 5 cm
Volume = (22/7) × 5² × 7 = 550 cm³
Total water transferred using small cylinder 6 times = 550 × 6 = 3300 cm³
Remaining volume to be filled in big vessel = 4400 - 3300 = 1100 cm³
Big vessel volume = π × r² × h
⇒ 1100 = (22/7) × 10² × h
⇒ 1100 = (22/7) × 100 × h
⇒ 1100 = (2200/7) × h
h = 1100 × 7/2200 = 3.5 cm