A cylindrical tank of radius 14 cm is full of water. If 616 litres of water are drawn out, then the water level in the tank is dropped by ______ m. (Take π = 22⁄7)

Correct — B. The stem is printed as an image: a cylindrical tank of radius 14 cm, full of water, from which 616 litres are drawn out, with π taken as 22⁄7 and the blank measured in metres.

Base area = πr² = 22⁄7 × 14² = 616 cm²
Volume drawn = 616 litres = 616 × 1000 = 6,16,000 cm³
Drop = volume ⁄ base area = 6,16,000 ⁄ 616 = 1000 cm

The blank wants metres, so 1000 cm = 10 m → option (b)

Why the others are wrong

• (a)
  1 — 1 — what you get by treating 616 litres as 616 cm³. One litre is 1000 cm³, so the volume drawn is 6,16,000 cm³ and the drop is a thousand times larger.
• (c)
  1000 — 1000 — the drop in centimetres, correct arithmetic halted one line early. The blank in the stem is followed by m, so the figure must be converted.
• (d)
  100 — 100 — 1000 cm converted with the wrong factor. 100 cm make a metre, not 10, so 1000 cm is 10 m and not 100 m.

When water leaves a vertical cylinder the surface stays flat and the base area never changes, so the volume removed is base area × drop in height.

That reduces the whole question to one division: h = V ⁄ πr². Nothing about the tank's own height is needed, and it is not given.

The numbers are built to cancel. A radius that is a multiple of 7 clears the 7 in 22⁄7 exactly, so 22⁄7 × 196 comes out as a whole 616 cm² with nothing left over.

Key facts

• 1 litre = 1000 cm³, and 1 metre = 100 cm.
• With π = 22⁄7 and r = 14 cm, the base area πr² is exactly 616 cm².
• For a vertical cylinder, the drop in level equals the volume removed divided by the base area.

Common traps

• Dividing 616 litres by 616 cm² without converting litres to cubic centimetres
• Answering 1000 because the working was done in centimetres and the blank asks for metres
• Using the curved surface area 2πrh in place of the base area πr²

No directly related past PYQ was found.