Chapter-5 (Area And Volume) Formulae

Area and Volume: Important Formulas

Mathematics • Grade 10 • Area and Volume

Quick memory: Pyramid and cone volumes are ⅓ of the prism or cylinder with the same base and height.

1. Square Based Pyramid

• Slant heightl² = h² + (a/2)²
• Edgee² = l² + (a/2)²
• Lateral surface areaLSA = 2al
• Total surface areaTSA = a² + 2al
• VolumeV = ⅓ a²h

2. Cone

• Slant heightl² = h² + r²
• Curved surface areaCSA = πrl
• Total surface areaTSA = πr² + πrl = πr(r + l)
• VolumeV = ⅓ πr²h
• Circumference of base = 2πr  |  Base area = πr²

3. Combined Solids

Solid	TSA	Volume
Cylinder + Cone	πr² + 2πrh₁ + πrl	πr²(h₁ + ⅓h₂)
Cone + Hemisphere	πr(l + 2r)	⅓πr²(h + 2r)
Cylinder + Hemisphere	2πrh + 3πr²	πr²(h + ⅔r)
Cone + Cone	πr(l₁ + l₂)	⅓πr²(h₁ + h₂)
Prism + Pyramid	a² + 4ah₁ + 2al	a²(h₁ + ⅓h₂)

4. Cost Estimation and Units

• Quadrilateral areaA = ½ × d × (p₁ + p₂)
• 4 walls + ceilingA = 2h(l + b) + lb
• CostTotal cost = Area × Rate
• 1 m³ = 1000 litres  |  1 ft³ = 28.317 litres  |  π = 22/7

Quick triples (h, half-base or r, l)
3, 4, 5  |  5, 12, 13  |  6, 8, 10  |  7, 24, 25  |  8, 15, 17  |  9, 12, 15

Exam tips: (1) Find l first. (2) Tents and pillars: leave out the base. (3) Halve diameter to get r. (4) Combined solids: add volumes, but do not add hidden faces.

Area and Volume • Grade 10 Mathematics