Surface Area, Volume and Capacity
ICSE Class 8 · Mathematics · Chapter 21
What this chapter covers
- Solids, faces and nets
- Surface area of a cuboid
- Surface area of a cube
- Curved and total surface area of a cylinder
- Volume and its basic unit
- Volume of a cuboid and a cube
- Volume of a cylinder
- Volume and capacity: units and conversion
- Surface area or volume: choosing the right idea
Key points
- Surface area is the total area covering a solid, measured in square units (cm², m²).
- Cuboid: TSA = 2(lb + bh + hl); lateral surface area = 2(l + b)h.
- Cube: TSA = 6a2; lateral surface area = 4a2.
- Cylinder: CSA = 2π r h; TSA = 2π r(h + r); an open cylinder has only one end.
- Volume is the space a solid occupies, measured by counting unit cubes, in cubic units (cm³, m³).
- Cuboid: V = lbh; cube: V = a3; cylinder: V = π r2 h. Each is base area × height.
- Capacity is the volume of the space inside a container; use inner measurements.
- 1 cm³ = 1 mL, 1000 cm³ = 1 L, and 1 m³ = 1000 L.
- Covering the outside needs surface area; filling the inside needs volume or capacity.
Questions answered
Find the total surface area of a cuboid 12 cm long, 8 cm wide and 5 cm high.
2(96 + 40 + 60) = 2 × 196 = 392 cm2.
Find the total surface area of a cube of edge 9 cm.
6 × 81 = 486 cm2.
Find the curved surface area of a cylinder of radius 14 cm and height 20 cm.
2 × (22)/(7) × 14 × 20 = 88 × 20 = 1760 cm2.
A closed cylindrical drum has a radius of 0.7 m and a height of 1.3 m. Find the cost of painting its whole outer surface at ₹30 per m².
TSA = 2 × (22)/(7) × 0.7 × (1.3 + 0.7) = 4.4 × 2 = 8.8 m2; cost = 8.8 × 30 = ₹264.
Why is a cube, and not a sphere, used as the unit of volume?
Equal cubes fit together with no gaps or overlaps, so counting them measures the space exactly; spheres always leave gaps.
The volume of a cube is 343 cm³. Find its edge.
7 × 7 × 7 = 343, so the edge is 7 cm.
A cuboid has a volume of 720 cm³, a length of 15 cm and a breadth of 8 cm. Find its height.
15 × 8 = 120, and 720 ÷ 120 = 6 cm.
A tank is 3 m long, 2 m wide and 1.5 m deep. Find its capacity in litres.
3 × 2 × 1.5 = 9 m3 = 9000 L.