Surface Area of Cubes Cuboids and Prisms

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Surface Area of Cubes Cuboids and Prisms — Free MYP3 Mathematics Practice Questions

1QuestionSolving Surface Area Problems in ContextConcept Practice

2 marks~3 minCriterion A

The net of a cuboid has side lengths of 3 cm, 4 cm, and 5 cm.

Calculate the area of each different rectangular face of the cuboid. [1]

Calculate the total surface area of the cuboid. [1]

Solutions

2QuestionUnderstanding Surface Area ConceptuallyAssessment Practice

3 marks~5 minCriterion B

The graph shows how the surface area of a cube changes as its side length increases from 1 cm to 5 cm.

Side length (cm)	1	2	3	4	5
Surface area (cm²)	6	24	54	96	150

State the formula for the surface area of a cube with side length

s

. Use it to calculate the surface area when

s = 4

cm. [1]

Explain why the surface area does not increase by the same amount each time the side length increases by 1 cm. [1]

The side length doubles from 2 cm to 4 cm. Analyse what happens to the surface area and explain why this result is not a surprise given the formula. [1]

Solutions

3QuestionUnderstanding Surface Area ConceptuallyAssessment Practice

5 marks~8 minCriterion C

An L-shaped prism is formed by joining Prism A (dimensions

3 \text{ cm} \times 4 \text{ cm} \times 5 \text{ cm}

) and Prism B (dimensions

3 \text{ cm} \times 2 \text{ cm} \times 5 \text{ cm}

) along a

3 \text{ cm} \times 5 \text{ cm}

face. The surface area of Prism A alone is

94 \text{ cm}^2

and of Prism B alone is

62 \text{ cm}^2

Calculate the area of the shared face. [1]

Explain why the total surface area of the L-shaped prism is not

94 + 62 = 156 \text{ cm}^2

. [2]

Draw a net of the L-shaped prism, label the hidden faces, and calculate the correct surface area. [2]

Solutions

4QuestionSolving Surface Area Problems in ContextAssessment Practice

6 marks~9 minCriterion D

A packaging company designs a rectangular box with length 20 cm, width 15 cm, and height 10 cm to hold a fragile cylindrical object with radius 6 cm and height 9 cm. The surface area of the box is found using:

S = 2(lw + lh + wh)

Calculate the total surface area of the box. [2]

Explain why the box dimensions are sufficient to contain the cylinder. [1]

Explain two reasons why the surface area formula alone may underestimate the amount of cardboard needed to manufacture this box. [3]

Solutions

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