Surface Area of Cubes Cuboids and Prisms
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Surface Area of Cubes Cuboids and Prisms — Free MYP2 Mathematics Practice Questions

1QuestionSolving Surface Area Problems in ContextConcept Practice
2 marks~3 minCriterion A

Data


- Front face: 6 cm6 \, \text{cm} wide, 3 cm3 \, \text{cm} tall
- Top face: 6 cm6 \, \text{cm} long, 4 cm4 \, \text{cm} wide
- Left side face: 4 cm4 \, \text{cm} wide, 3 cm3 \, \text{cm} tall
The net of a cuboid is shown below. Three faces are labelled with their dimensions.

Dimensions
a
Identify the width of the back face of the cuboid. [1]
b
Explain how you know the back face and front face must have the same dimensions. [1]
Question diagram

Solutions

2QuestionUnderstanding Surface Area ConceptuallyAssessment Practice
3 marks~5 minCriterion B
The graph shows the surface area of a cube with side length ss (cm), using the formula SA=6s2SA = 6s^2.
a
Identify the shape of the graph. [1]
b
Explain why the surface area increases faster than the side length. [1]
c
Compare the surface area when s=2s = 2 cm and when s=4s = 4 cm. What does this tell you about how surface area grows? [1]
Question diagram

Solutions

3QuestionSolving Surface Area Problems in ContextAssessment Practice
4 marks~6 minCriterion D
A student wants to wrap a gift box shaped like a rectangular prism with these dimensions:

Length (l)(l): 20 cm, Width (w)(w): 15 cm, Height (h)(h): 10 cm

The surface area formula is:
S=2(lw+lh+wh)S = 2(lw + lh + wh)
a
Calculate the surface area of the box. Show all working. [2]
b
Identify and explain two limitations of using this formula to estimate the amount of wrapping paper needed. In your answer, state one assumption the formula makes about the shape of the box. [2]
Question diagram

Solutions

4QuestionSurface Area of a Rectangular PrismAssessment Practice
6 marks~9 minCriterion C
A student calculates the surface area of a rectangular prism (l=8l = 8 cm, w=5w = 5 cm, h=3h = 3 cm) as shown:

SA=2(8×5)+2(5×3)=80+30=110 cm2SA = 2(8 \times 5) + 2(5 \times 3) = 80 + 30 = 110 \text{ cm}^2
a
Identify the missing term in the student's calculation. [1]
b
Explain why the formula SA=2lw+2lh+2whSA = 2lw + 2lh + 2wh accounts for all six faces of the prism. Use the net diagram provided to support your answer. [2]
c
Calculate the correct surface area. Show each step clearly. [3]
Question diagram

Solutions

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