Surface area and volume answer two different questions about the same solid: how much material covers it, and how much space it holds. Students who keep them separate rarely go wrong; students who blur them lose marks on almost every question.
SA = 2(lw + lh + wh) · V = l × w × h
Surface area adds the areas of all six faces of a rectangular prism. Because the faces come in matching pairs, you can find the area of three different faces, add them, and double the total. Volume, by contrast, multiplies the three dimensions together.
Find the surface area of a box 5 cm × 4 cm × 3 cm.
Answer: 94 cm²
Find the surface area of a cube with edge 6 cm.
Answer: 216 cm²
A prism is 10 cm × 2 cm × 2 cm. Find its volume and its surface area.
Answer: V = 40 cm³ and SA = 88 cm²
Work through these in order. Each answer opens to show the full method, so you can check your reasoning rather than just your final number.
Find the surface area of a cube with edge 3 cm.
Answer: 54 cm²
Each face is 3 × 3 = 9 cm², and there are 6 faces: 6 × 9 = 54 cm².
Find the volume of a prism 4 cm × 3 cm × 2 cm.
Answer: 24 cm³
V = 4 × 3 × 2 = 24 cm³.
Find the surface area of a box 2 cm × 2 cm × 5 cm.
Answer: 48 cm²
Faces: 4, 10, 10. Sum is 24, doubled gives 48 cm².
A cube has edge 10 cm. Find its volume.
Answer: 1000 cm³
V = 10 × 10 × 10 = 1000 cm³.
Find the surface area of a prism 7 cm × 5 cm × 2 cm.
Answer: 118 cm²
Faces: 35, 14, 10. Sum is 59, doubled gives 118 cm².
A cube has surface area 96 cm². Find the length of one edge.
Answer: 4 cm
Each face is 96 ÷ 6 = 16 cm², and √16 = 4 cm.
A box 6 cm × 4 cm × 5 cm is to be wrapped. How much paper is needed?
Answer: 148 cm²
Faces: 24, 30, 20. Sum is 74, doubled gives 148 cm².
A cube has volume 64 cm³. Find its surface area.
Answer: 96 cm²
The edge is the cube root of 64, which is 4. Each face is 16 cm², so 6 × 16 = 96 cm².
Two cubes have edges 2 cm and 4 cm. How many times greater is the larger surface area?
Answer: 4 times
Surface areas are 24 cm² and 96 cm². Since 96 ÷ 24 = 4, area scales with the square of the edge ratio.
A prism has square base of side 3 cm and volume 45 cm³. Find its surface area.
Answer: 78 cm²
Base area is 9, so height is 45 ÷ 9 = 5. Faces: 9, 15, 15. Sum is 39, doubled gives 78 cm².
Generate a surface area and volume test at the grade and difficulty you need, with a complete worked answer key and equivalent versions for retakes.
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Exam questions rarely use the words surface area or volume. They ask how much wrapping paper is needed, how much paint covers a shed, how much water a tank holds, or how many cubes fit inside. The first two are surface area; the last two are volume. Training students to classify the question before touching a formula is worth more than drilling either formula in isolation.
A useful test is to ask whether the answer describes something flat or something filled. Paint sits on a surface, so the answer is flat and the units are square. Water fills a space, so the answer is three-dimensional and the units are cubic. Students who check units at the end catch most of their own errors.
Doubling every edge of a cube multiplies its surface area by four and its volume by eight, because area depends on two dimensions and volume on three. This is not a curiosity; it is the reason large animals overheat less easily than small ones and why sugar dissolves faster when it is ground finer.
In exam terms, it means a scale factor question about area uses the square of the ratio and one about volume uses the cube. Students who memorise the two formulas but not this relationship lose marks on the highest-value questions in the topic.
✗ Using cubic units for surface area.
✓ Surface area is a total of flat areas, so the units are square: cm², not cm³.
✗ Forgetting to double the sum of the three face areas.
✓ A rectangular prism has six faces in three matching pairs, so the sum of three distinct faces must be doubled.
✗ Using the volume formula when the question asks about covering or painting.
✓ Covering, painting and wrapping are all surface area. Filling and holding are volume.
✗ Assuming a larger volume always means a larger surface area.
✓ A long thin prism can hold less than a cube yet have far more surface area, as the 10 × 2 × 2 example shows.