The curved surface area (CSA) of a cylinder is the area of its lateral (side) surface, excluding the two circular bases. Formula: CSA = 2πrh, where r is the radius of the base and h is the height. The total surface area (TSA) includes both circular bases: TSA = 2πr(r + h). Volume = πr²h.
CSA of cylinder = 2πrh (curved/lateral surface only).
TSA of cylinder = 2πr(r+h) (includes both circular bases).
Volume of cylinder = πr²h.
CSA is obtained by unrolling the lateral surface into a rectangle of dimensions 2πr × h.
π = 22/7 is commonly used in calculations.
For a pipe (hollow, open cylinder): use CSA = 2πrh.
Curved Surface Area (CSA) = 2πrh Also called: Lateral Surface Area (LSA)
Where: • r = radius of the circular base • h = height (length) of the cylinder • π ≈ 3.14159 or 22/7
Derivation: If the cylinder is 'unrolled' (lateral surface unrolled into a flat sheet), it forms a rectangle: • Length of rectangle = circumference of circle = 2πr • Width of rectangle = height of cylinder = h • Area of rectangle = 2πr × h = 2πrh
Total Surface Area (TSA): TSA = CSA + 2 × (area of one circular base) = 2πrh + 2πr² = 2πr(h + r)
Volume: V = πr²h
Example 1: A cylinder has radius 7 cm and height 10 cm. Find CSA and TSA.
CSA = 2πrh = 2 × (22/7) × 7 × 10 = 2 × 22 × 10 = 440 cm²
TSA = 2πr(r+h) = 2 × (22/7) × 7 × (7+10) = 2 × 22 × 17 = 748 cm²
Volume = πr²h = (22/7) × 7² × 10 = 22 × 7 × 10 = 1540 cm³
Example 2: CSA of cylinder = 880 cm², radius = 10 cm. Find height. 2πrh = 880 2 × (22/7) × 10 × h = 880 (440/7) × h = 880 h = 880 × 7/440 = 14 cm
Example 3: Diameter = 14 cm, h = 20 cm. Radius r = 7 cm. CSA = 2 × (22/7) × 7 × 20 = 880 cm² TSA = 2 × (22/7) × 7 × (7+20) = 2×22×27 = 1188 cm²
For a cylinder with radius r and height h:
CSA (Curved/Lateral Surface Area) = 2πrh TSA (Total Surface Area) = 2πr(r + h) Area of one circular base = πr² Volume = πr²h Diagonal of cylinder = √(4r² + h²)
Note: • CSA does NOT include the two circular ends. • TSA includes both circular ends. • Open cylinder (like a pipe) → use CSA. • Closed cylinder (like a can) → use TSA.
Useful values of π: • π = 22/7 (fraction approximation) • π ≈ 3.14 (decimal approximation) • π ≈ 3.14159265... (more precise)
CSA of cylinder = 2πrh, where r is the radius of the base and h is the height. This represents the lateral surface only, excluding the two circular bases.
CSA (Curved Surface Area) = 2πrh — the lateral surface only. TSA (Total Surface Area) = 2πr(r+h) = CSA + 2πr² — includes both circular bases. TSA = CSA + (area of two circles).
CSA = 2πrh = 2 × (22/7) × 7 × 10 = 440 cm².
When the lateral surface of a cylinder is unrolled, it forms a rectangle. The length of this rectangle is 2πr (the circumference of the circular base) and the width is h (the height). Area = length × width = 2πr × h = 2πrh.
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