Surface Area & Volume
Cylinders, prisms and pyramids
Surface Area and Volume of Cylinders, Prisms and Pyramids
Cylinder: V = πr²h, SA = 2πr² + 2πrh.
Prism: V = base area × height.
Pyramid: V = ⅓ × base area × height.
Surface area = sum of all faces (use nets to visualise).
Example
Cylinder
Radius = 5 cm, height = 10 cm.
Volume = π(5)²(10) = 250π ≈ 785.4 cm³
Surface area = 2π(5)² + 2π(5)(10)
= 50π + 100π = 150π ≈ 471.2 cm²
Example
Square-Based Pyramid
Base side = 6 cm, height = 8 cm, slant height = 10 cm.
Volume = ⅓ × (6×6) × 8 = ⅓ × 288 = 96 cm³
SA = base + 4 triangular faces
= 36 + 4(½ × 6 × 10) = 36 + 120 = 156 cm²
Note
Remember
Cylinder = circular prism. Pyramid volume is ⅓ of the prism with the same base and height. Use π ≈ 3.14 or leave answers in terms of π. Always include units (cm³ for volume, cm² for surface area).
Key Vocabulary
CylinderA 3D shape with circular top and bottom joined by a curved surface
PyramidA 3D shape with a flat base and triangular faces meeting at a point
RadiusDistance from centre to edge of a circle
Slant heightThe distance along a slanted face of a pyramid or cone
Pi (π)A constant ≈ 3.14159, the ratio of circumference to diameter
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Cylinder
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