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Surface Area and Volume of 3D Solids Summary — Free MYP4 Mathematics (Extended) Practice Questions
1QuestionSurface Area of Cylinders and PrismsConcept Practice
3 marks~5 minCriterion A
A manufacturer produces cylindrical tins for storing loose-leaf tea. Each tin has a radius of 4 cm and a height of 10 cm. The total surface area of a cylinder is given by . Use .
a
Calculate the area of the two circular bases of the tin. [1]
b
Calculate the total surface area of the tin. [1]
c
A rectangular sheet of decorative paper measuring 30 cm by 28 cm is available to wrap the tin entirely. Justify whether this sheet is large enough to cover the total surface area of the tin. [1]
Solutions
2QuestionNets and Surface Area of Cubes and CuboidsAssessment Practice
2 marks~3 minCriterion D
A company designs a cardboard box for shipping a laptop. The box is a cuboid with dimensions 40 cm by 30 cm by 5 cm. The cost of cardboard is 0.02 dollars per .
Identify one assumption made when using the surface area of the cuboid to estimate the total cost of cardboard, and explain why this assumption could make the estimate inaccurate. (Do not calculate the cost.) [2]
Identify one assumption made when using the surface area of the cuboid to estimate the total cost of cardboard, and explain why this assumption could make the estimate inaccurate. (Do not calculate the cost.) [2]
Solutions
3QuestionVolume of Cubes Cuboids and CylindersAssessment Practice
4 marks~6 minCriterion C
A manufacturer drills a cylindrical hole vertically through the centre of a solid wooden cube to reduce its mass. The cube has side length 6 cm. The cylindrical hole has radius 2 cm and passes completely through the cube from top face to bottom face.
a
Calculate the volume of the cube. [1]
b
Calculate the volume of material removed by the cylindrical hole, giving your answer in the form cm³. [1]
c
The manufacturer claims that more than 35% of the cube's volume has been removed. Justify whether this claim is correct. [2]
Solutions
4QuestionNets and Surface Area of Cubes and CuboidsAssessment Practice
5 marks~8 minCriterion B
Five nets of six squares are shown in the diagram.
Net A: cross shape (central column of 4 squares, one square attached left and one right of the second square from the top)
Net B: T-shape (row of 4 squares with one square attached above and one below the second square)
Net C: strip (all 6 squares in a single row)
Net D: rectangle
Net E: L-shape (row of 3 squares with a further row of 3 squares attached perpendicularly at one end)
Net A: cross shape (central column of 4 squares, one square attached left and one right of the second square from the top)
Net B: T-shape (row of 4 squares with one square attached above and one below the second square)
Net C: strip (all 6 squares in a single row)
Net D: rectangle
Net E: L-shape (row of 3 squares with a further row of 3 squares attached perpendicularly at one end)
a
Classify each net as valid or invalid for folding into a cube. [1]
b
For each invalid net, justify why it cannot fold into a cube, referring to overlap or face-adjacency. [2]
c
A packaging engineer claims that any connected arrangement of exactly 6 squares can fold into a cube. Critique this claim, and state the precise condition a net must satisfy to be a valid cube net. [2]
Solutions
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