Volume and surface area

Volume and surface area

Pencil and paper
Overview
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about surface area and volume of cuboids.

Diagram 1

a) What is the area of the net in Diagram 1? _________ cm2
 
The net is made up into a cube, which is shown in Diagram 2.

Diagram 2

b) i)
What is the volume of the cube? __________ cm3
 
  ii) What is the surface area of the cube? ________ cm2
 
Diagram 3 shows two of the cubes glued together.

Diagram 3

c) i)
What is the combined volume of the two cubes? _________ cm3
 
  ii) What is the surface area of the two cubes now that they are glued together? ________ cm3
Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
area, surface area, volume, cuboids
Description of task: 
Students calculate the surface area and volume of cuboids.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Measurement sense, sets 7-8
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
   

Y10 (12/1997)
a)   54  moderate
b) i)
ii)		 27 
54 		 easy
difficult
c) i)
ii)		 54 
90 		 easy
difficult
Diagnostic and formative information: 
  Student response Likely calculation Likely reason
a) 42 14 × 3 Confuses area and perimeter.
a) 36 6 × (3 + 3) Calculates area of each square as 3 + 3, i.e., confuses area and perimeter.
b) i)
c) i)		 9
18		 3 + 3 + 3
2 × 9		 Calculates volume by adding rather than multiplying dimensions.
b) ii) 9 3 × 3 Surface area of one face only.
c) ii) 108 2 × 54 Fails to subtract nine for each of the two hidden faces.