The radius and height of a solid cylinder is 8 cm and 14 cm respectively. Find, correct to two d.p the total surface area. (Take $\pi = \frac{22}{7})$

Analyze the question: We need the total surface area of a closed solid cylinder with r = 8 cm and h = 14 cm, using π = 22/7.

Concept: Total surface area of a cylinder = 2πr(h + r), which is the curved surface (2πrh) plus the two circular ends (2πr²).

Solution:

• 2πr(h + r) = 2 × (22/7) × 8 × (14 + 8)
• = 2 × (22/7) × 8 × 22
• = (2 × 22 × 8 × 22) / 7
• = 7744 / 7
• = 1106.285714...

Correct to 2 d.p.: 1,106.29 cm²

Check using the separate parts:

• Curved surface: 2 × (22/7) × 8 × 14 = 704 cm²
• Two circular ends: 2 × (22/7) × 64 = 1408/7 ≈ 201.29 cm²
• Total: 704 + 201.29 = 905.29 cm²

That doesn't match, so let me recheck. 2πrh = 2 × (22/7) × 8 × 14 = 2 × 22 × 8 × 2 = 704. Correct. The ends: 2πr² = 2 × (22/7) × 64 = 2816/7 ≈ 402.29 cm² (I previously miscalculated 1408/7, which is only one end).

Total: 704 + 402.29 = 1,106.29 cm² ✔

Answer: Option A, 1,106.29 cm²

Tip: Factor first: 2πr(h + r). Here h + r = 22, which cancels neatly with the 7 pattern of π = 22/7 and saves time. Also, watch out for "total" vs "curved" surface area: total includes both circular ends.