Three oranges

Three oranges

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
This task is about working out height, area and volume.

Three-oranges.png
   

Useful Information

Area of circle = πr2

Volume of cylinder = area of base × height

Volume of sphere = 4⁄3πr3

Use π = 3.14
Three oranges (perfect spheres), each with a radius of 4 cm, are packaged one on top of the other in a clear plastic tube for export.
   

Question 2Change answer

a)  What is the height of the tube?  cm

Question 2Change answer

b)  What is the area of the lid of the cylinder?  cm2

Question 2Change answer

c)  What is the volume of the empty cylinder?  cm3

Question 2Change answer

d)  What is the volume of one orange?  cm3

Question 2Change answer

e)  What is the volume of air in the cylinder when all 3 oranges are in it?  cm3
Task administration: 
This task can be completed with pencil and paper or online (with SOME auto marking).
Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
spheres, circles, cylinders, area, volume
Description of task: 
Students use a diagram of, and information about oranges packed in a cylinder to calculate height, area and volume.
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 (11/99)

a)

24

moderate

b)

50.24 [accept 50.2 to 50.3]

moderate

c)

1205.76 [accept 1205 to 1207 or
answer to a) × answer to b)]

moderate

d)

267.95 [accept 267.5 to 268.5]

difficult

e)

401.92 [accept 400 to 404 or
answer to c) – (3 × answer to d))]

difficult

 

Diagnostic and formative information: 

  

Common error

Likely calculation

Likely reason

a)

12

4 × 3

Uses radius rather than diameter.

b)

12.56
25.12

4 × π or π.22
8 × π = 2 × 4 × π

Confuses radius and diameter.
Calculates circumference rather than area.

d)

50.24

66.98 to 67.05

π × 42

1⁄3πr3

Confuses area and volume.

Ignores the 4 in the equation for the volume of a cylinder.