A cylinder is not a prism but has a similar structure.
The formula for the volume of a cylinder can be derived by using the formula for a prism.
This can be used to find the volume of any cylinder.
Unknown lengths can be found when the volume of a cylinder is known.

Common misconception

When questions are in context, the height of the cylinder may be described as the depth or length and this can cause some pupils to struggle if they have learned a formula with a particular word.

Remind pupils that the volume of a 3D shape comes from a product of three perpendicular lengths. The cross-sectional area uses two of the three, so identify the distance that is perpendicular to the cross-sectional face.

Keywords

Cylinder - A cylinder is a 3D shape with a base that is a circle and a parallel opposite face that is identical. A cross-section of a cylinder made parallel to the base will be congruent to the base.
Volume - Volume is the amount of space occupied by a closed 3D shape.

Encourage pupils to clearly label on diagrams and in their solutions, if they have been given the radius or diameter of the circular cross-section.

Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.

This prism has two congruent regular octagonal faces and congruent rectangular faces.

Correct Answer: eight, 8

Q2.

Izzy takes some measurements from a cube. Match each measurement to its correct value.

Correct Answer:Area of cross-section,25 cm²

25 cm²

Correct Answer:Length of one side,5 cm

5 cm

Correct Answer:Perimeter of cross-section,20 cm

20 cm

Correct Answer:Surface area,150 cm²

150 cm²

Correct Answer:Volume,125 cm³

125 cm³

Q3.

The surface area of this octagonal prism is cm².

Correct Answer: 668

Q4.

The diagram shows a prism unfolded into its net. The perimeter of the cross-sectional face is 70 cm. Which of these statements are correct?

Dimensions of rectangle in the net: 6 cm by 320 cm

Correct answer: Dimensions of rectangle in the net: 6 cm by 70 cm

Total surface area = (320 + 5 × 70) cm²

Correct answer: Total surface area = (2 × 320 + 70 × 6) cm²

Total surface area = (2 × 320 + 5 × (70 × 6)) cm²

Q5.

The diagram shows the net of a triangular prism. The depth of the prism is 4 cm. The surface area of the prism that can be formed from this net is cm².

Correct Answer: 144

Q6.

The cross-section of this prism is an equilateral triangle. The surface area of this triangular prism is cm². Give your answer correct to 3 significant figures.