Volume of Cubes Prisms and Cylinders

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Volume of Cubes Prisms and Cylinders — Free MYP2 Mathematics Practice Questions

1QuestionIntroduction to Volume of CylindersConcept Practice

2 marks~3 minCriterion A

A cylinder has a diameter of 10 cm and a height of 8 cm.

Identify the radius of the cylinder. [1]

Calculate the volume of the cylinder using

V = \pi r^2 h

. [1]

Solutions

2QuestionIntroduction to Volume of CylindersAssessment Practice

3 marks~5 minCriterion C

A cylinder has a fixed height of 5 cm. Its volume is given by

V = \pi r^2 h

where

r

is the radius and

h

is the height.

Identify the part of the formula that shows volume is not directly proportional to the radius. [1]

Explain why the graph of

V

against

r

is a curve rather than a straight line. [1]

Two cylinders both have height 5 cm. Cylinder A has radius 2 cm and Cylinder B has radius 4 cm. The radius of B is twice the radius of A. Compare the volumes and explain why the volume of B is not simply twice the volume of A. [1]

Solutions

3QuestionVolume of a CubeAssessment Practice

3 marks~5 minCriterion B

The table shows the volume of cubes with different edge lengths.

Edge length (cm)	1	2	3	4
Volume (cm³)	1	8	27	64

Identify the relationship between the edge length

s

and the volume

V

of a cube. [1]

Calculate the volume of a cube with an edge length of 5 cm. [1]

A second cube has a volume of 64 cm³ and a third cube has a volume of 125 cm³. Compare the edge lengths of these two cubes. [1]

Solutions

4QuestionIntroduction to Volume of CylindersAssessment Practice

4 marks~6 minCriterion D

A paint factory fills cylindrical cans using the formula

V = \pi r^2 h

Each can has a radius of 7 cm and a height of 20 cm. Use

\pi \approx \dfrac{22}{7}

Calculate the volume of one can. [1]

Each can is filled to only 90% of its full capacity. Calculate the volume of paint in one can. [1]

Explain whether the formula overestimates or underestimates the actual volume of paint in the can, and identify one real-world reason why leaving an air gap is necessary. [2]

Solutions

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