Volume of cuboids

Volume of cuboids

Auto-markingPencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
This task is about working out the volume of some cuboids.
boxes.png
[Not drawn to scale]
Sarah found two boxes to pack things in. The dimensions of each box are shown above.

Question 2Change answer

a)  What is the volume of 
     i)   Box A?  cm3

     ii)  Box B?  cm3

Question 2Change answer

b)  Sarah was packing small parcels into two large boxes to post overseas.
     What is the greatest number of small parcels with the dimensions 5 cm × 4 cm × 7 cm that Sarah could fit in Box A?
     
Task administration: 
This task can be completed with pencil and paper or online (with auto marking displayed to students).
Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
volume, cuboids
Description of task: 
Students use diagrams of two boxes with given dimensions to calculate the volume of both boxes and the number of smaller boxes that could fit into one of the boxes.
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 (11/1999)

a)

i)
ii)

5600
7200

easy
easy

b)

 

40

easy
Diagnostic and formative information: 

 

Common error

Likely calculation

Likely reason

a)i)
   ii)

54
59

20 + 20 + 14
25 + 18 + 16

Adds rather than multiplies the dimensions.

b)i)

140

5 × 4 × 7

Gives the volumes of the small parcels.
Next steps: 
Extension
What is the greatest number of small parcels with the dimensions 
4 cm × 4 cm × 4 cm that Sarah could fit in Box B?
Answer: 96. Common wrong answers are 112, 112.5. These ignore the fact that not all the space in Box B can be utilised. (112.5 = 7200 ÷ 64)