The volume of a right circular cylindrical box of radius 30cm is 600cm³. Find the height of the box.

Correct — A. For a right circular cylinder V = πr²h, so h = V ⁄ (πr²).

Base area first, with r = 30 cm:
r² = 900
πr² = (22⁄7) × 900 = 19,800⁄7 ≈ 2,828.57 cm²

Now divide the volume by it:
h = 600 ⁄ 2,828.57 = 0.2121…

To two decimal places h = 0.21 cm → option (a). (Using π = 3.1416 gives 0.2122, the same answer.)

Why the others are wrong

• (b)
  0.61cm — 0.61 cm would hold 0.61 × 2,828.57 ≈ 1,725 cm³, nearly three times the 600 cm³ the stem fixes.
• (c)
  0.51cm — 0.51 cm would hold about 1,443 cm³. Multiplying any option by the base area is the fastest check when the choices are this close.
• (d)
  0.31cm — 0.31 cm would hold about 877 cm³, nearly half as much again as the 600 cm³ the stem fixes.

A cylinder is a base area repeated through a height, so its volume is πr²h and nothing else.

When the radius is large and the volume small, the height is tiny. Here the base alone is about 2,829 cm², while the whole box holds 600 cm³ — so the box is about 2 mm deep, a disc rather than a tin.

Expect a sensible-looking height in centimetres and you may hunt for an error that is not there.

Key facts

• Volume of a right circular cylinder: V = πr²h.
• Curved surface area is 2πrh and total surface area is 2πr(r + h) — neither is the volume.
• With r = 30 cm the base area is 900π ≈ 2,827 cm², far larger in number than the 600 cm³ volume, so h must be well under 1 cm.
• 600 ⁄ (900π) = 0.2122 cm, which is 0.21 cm to two decimal places.

Common traps

• Using the given 30 cm as the diameter instead of the radius
• Reaching for 2πrh when the stem supplies a volume
• Rejecting a sub-centimetre height as impossible and re-doing correct work

No directly related past PYQ was found.