Last reviewed: 10 November 2026
Updated November 2026. These Grade 8 nets and surface area notes explain how to sketch nets of cubes, cuboids, cylinders, pyramids and cones, and how to use a net to work out surface area. A net is the flat shape you get when you unfold a solid. The surface area is the total area of all the faces, which is the area of the net. A cube of side 5 cm has six square faces, so its surface area is 6 × 5 × 5 = 150 cm².
The examples and questions are original practice for Kenyan junior school learners, not an official paper. For the other Grade 8 maths topics, see our Grade 8 mathematics revision guide and the Grade 8 notes hub.
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What the Grade 8 Curriculum Covers
Common solids is a sub-strand under Geometry in the Kenya Institute of Curriculum Development’s Grade 8 Mathematics design. Learners identify common solids, sketch nets of cubes, cuboids, cylinders, pyramids and cones, work out surface area from nets, and make models of hollow and compact solids. The design is listed on the KICD Grade Eight curriculum designs page.
Nets of Common Solids
| Solid | Net is made of |
|---|---|
| Cube | 6 equal squares |
| Cuboid | 3 pairs of equal rectangles |
| Cylinder (closed) | 2 circles and 1 rectangle |
| Square-based pyramid | 1 square and 4 triangles |
| Cone (closed) | 1 circle and 1 sector |
A cube has 11 different nets. A quick check: when folded, no two squares may land on the same face. Making a net from a cereal box or from manila paper is a good way to see how the faces fit.
Surface Area From Nets
Add the areas of every shape in the net. The formulas below match OpenStax Prealgebra’s section on volume and surface area.
Cuboid
Surface area = 2(lw + lh + wh). A box 8 cm by 5 cm by 3 cm: 2(40 + 24 + 15) = 2 × 79 = 158 cm².
Cylinder
The rectangle in the net has width equal to the height h and length equal to the circumference 2πr. Closed cylinder surface area = 2πr² + 2πrh.
Example: r = 7 cm, h = 10 cm, π = 22/7. Two circles: 2 × 22/7 × 49 = 308 cm². Curved surface: 2 × 22/7 × 7 × 10 = 440 cm². Total = 748 cm². An open-top tin uses only one circle: 154 + 440 = 594 cm².
Square-based pyramid
Base 6 cm by 6 cm; each triangular face has base 6 cm and slant height 5 cm. Base: 36 cm². Four triangles: 4 × ½ × 6 × 5 = 60 cm². Total = 96 cm². Use the slant height of the triangle, not the vertical height of the pyramid.
Cone
The curved surface unfolds into a sector with area πrl, where l is the slant height. For r = 7 cm and l = 10 cm: curved area = 22/7 × 7 × 10 = 220 cm². Adding the base circle (22/7 × 49 = 154 cm²) gives 374 cm² for a closed cone.
Hollow and Compact Solids
A hollow model (like a box made from a net) has only a surface; a compact model (like one made from clay or soap) is solid all through. The surface area of both is the same if their shapes and sizes match. Hollow models help you see nets; compact models help you see volume.
Real-Life Example
In this made-up example, a fundi is painting the outside of a closed cylindrical water tank of radius 0.7 m and height 2 m. Surface area = 2 × 22/7 × 0.49 + 2 × 22/7 × 0.7 × 2 = 3.08 + 8.8 = 11.88 m². If one litre of paint covers 6 m², about 2 litres are needed (11.88 ÷ 6 ≈ 1.98).
Original Practice Questions With Worked Answers
- Find the surface area of a cube of side 4 cm. 6 × 16 = 96 cm².
- Find the surface area of a cuboid 10 cm × 4 cm × 2 cm. 2(40 + 20 + 8) = 136 cm².
- How many faces of each shape are in the net of a triangular prism? 2 triangles and 3 rectangles.
- Find the curved surface area of a cylinder with r = 14 cm, h = 5 cm. 2 × 22/7 × 14 × 5 = 440 cm².
- A cone has r = 3.5 cm and slant height 6 cm. Find its curved surface area. 22/7 × 3.5 × 6 = 66 cm².
Cover the answers and attempt each question first. For timed practice, use the Grade 8 revision papers or the Grade 8 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
What is a net of a solid?
A flat shape that can be folded to make the solid. It shows every face laid out in one piece.
How do you find surface area from a net?
Find the area of each shape in the net and add them together.
What shapes make the net of a cylinder?
Two circles and one rectangle whose length equals the circumference of the circles.
What is the difference between a hollow and a compact solid?
A hollow solid has only an outer surface, like a box. A compact solid is filled all the way through, like a block of clay.