If the radius and height of a right circular cylinder are 21 cm and 5 cm, respectively, then the total surface area of the cylinder is (use π = 22⁄7):

Correct — A. The stem is an image: a right circular cylinder of radius 21 cm and height 5 cm, total surface area with π = 22 ⁄ 7.

Total surface area = 2πr(r + h) — the curved sheet plus both circular ends.
r + h = 21 + 5 = 26
2πr = 2 × 22 ⁄ 7 × 21 = 132
132 × 26 = 3432

That is option (a).

Why the others are wrong

• (b)
  5212 cm — 5212 divided by the circumference 132 gives r + h ≈ 39.5, a cylinder about 18.5 cm tall. The question sets the height at 5 cm.
• (c)
  3816 cm — 3816 implies r + h ≈ 28.9 once divided by 132, so a height near 7.9 cm. With r = 21 and h = 5 the bracket is exactly 26.
• (d)
  4312 cm — 4312 implies r + h ≈ 32.7, a height near 11.7 cm. With r = 21, π = 22 ⁄ 7 and a whole-number height, the total has to be a multiple of 132, and 4312 is not.

A closed right circular cylinder has three surfaces: the curved sheet, of area 2πrh, and two circles of area πr² each.

Adding them and factorising gives 2πr(r + h). Factorise before you multiply — 2 × 22 ⁄ 7 × 21 collapses to 132 in one step because 21 carries the 7.

Keep the two names apart: curved surface area is 2πrh alone, total surface area includes the ends. Most marks lost here are lost on that word.

Key facts

• Total surface area of a closed cylinder = 2πr(r + h), and curved surface area = 2πrh.
• With r = 21 and π = 22 ⁄ 7, the circumference 2πr is exactly 132.
• A radius that is a multiple of 7 cancels the 7 in 22 ⁄ 7 and keeps the arithmetic whole.
• The volume of the same cylinder would be πr²h = 6930, a different quantity from any surface area.

Common traps

• Answering with the curved surface area 2πrh = 660 instead of the total.
• Adding only one circular end, which gives 660 + 1386 = 2046.
• Reading 21 cm as the diameter, which would make r = 10.5 and the total 66 × 15.5 = 1023.

No directly related past PYQ was found.