A well with 14 cm radius is dug 23 cm deep. Find the volume of the earth taken out of it.

Correct — A. A well is a right circular cylinder, so the earth removed is πr²h with r = 14 cm and h = 23 cm.

r² = 14 × 14 = 196
πr² = 22⁄7 × 196 = 616
616 × 23 = 12320 + 1848 = 14,168

Volume = 14,168 cm³, printed on option (a) as '14,168 cm'.

Taking π as 22⁄7 is what keeps this exact — the 7 cancels into 14 and every step stays a whole number.

Why the others are wrong

• (b)
  14,108 cm — 14,108 sits 60 below the answer. 616 × 23 splits as 12,320 + 1,848 and both halves are needed — this option only survives if you stop comparing after the leading digits.
• (c)
  15,168 cm — 15,168 differs by exactly 1,000, a slip in the thousands column. For r = 14 and h = 23 the product πr²h is fixed at 14,168, so this is a copying error rather than a different method.
• (d)
  14,178 cm — 14,178 is 10 above the answer. Options this close are decided in the tens and units, so finish 616 × 23 exactly: 616 × 20 = 12,320 and 616 × 3 = 1,848.

A well sunk into the ground is a right circular cylinder, and the earth taken out is its volume, V = πr²h. Depth is the height.

Two habits make this a ten-second question. Use π = 22⁄7 whenever the radius is a multiple of 7, because the 7 cancels and the total comes out whole.

And read which dimension you were handed: 14 cm is the radius here, not the diameter. The question asks for the earth removed, so curved surface area, 2πrh, is not wanted.

Key facts

• Volume of a right circular cylinder = πr²h.
• With r = 14 cm, h = 23 cm and π = 22⁄7, the volume is 14,168 cm³.
• π = 22⁄7 cancels exactly whenever the radius is a multiple of 7.

Common traps

• Reading 14 cm as the diameter and halving it to 7 cm.
• Computing the curved surface area, 2πrh = 2,024, in place of the volume.
• Using π = 3.14, which returns 14,155.12 and matches no option.

No directly related past PYQ was found.