Directions: Read the following passage carefully and answer the question given…
2022
Directions: Read the following passage carefully and answer the question given below.
A hollow cylinder A of radius 14 cm is full of water and a solid cylinder B of radius 7 cm is put inside the hollow cylinder, after which the remaining quantity of water is 9240 cm3. The height of both cylinders is the same.
If there is a leak in cylinder B which can empty it at 0.5 cm3/sec, then in how much time will the cylinder be emptied? (in minutes)
- A.
112 ⅕ mins
- B.
112 ⅔ mins
- C.
102 mins
- D.
102 ⅖ mins
- E.
102 ⅔ mins
Show answer & explanation
Correct answer: E
Concept
The volume of a right circular cylinder is V = πr2h, where r is the radius and h the height. When a solid is fully submerged in a liquid-filled container of the same height, the liquid it displaces equals the solid's own volume; so the water left over is the difference between the container's volume and the solid's volume. Time to drain at a constant rate = (volume to drain) ÷ (rate).
Application
Let the common height be h. Remaining water = volume of A − volume of B = π(14)2h − π(7)2h = πh(196 − 49) = 147πh.
Set this equal to the given leftover: 147 × (22/7) × h = 9240 ⇒ 462h = 9240 ⇒ h = 20 cm.
Volume of solid cylinder B = π(7)2h = (22/7) × 49 × 20 = 3080 cm3.
Time to empty B = 3080 ÷ 0.5 = 6160 seconds = 6160 ÷ 60 = 308/3 = 102⅔ minutes.
Cross-check
Verify the leftover with h = 20: 147 × (22/7) × 20 = 462 × 20 = 9240 cm3, which matches the data. Draining 3080 cm3 at 0.5 cm3/sec confirms 102⅔ minutes.