Work out the area

Work out the area

Pencil and paper
Overview
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about using the diameters of tins to work out the floor area of a carton and a given number of tins.
a)


 
  Four paint tins each 12.5 cm in diameter, fit into a carton as shown. What is the area of the bottom of the carton?
 
  (A)
(B)
(C)
(D)
(E)		 50 cm²
100 cm²
625 cm²
1250 cm²
None of these. The answer is __________ cm².
 
b)


 
  The 6 smaller paint tins packed in this carton each have a radius of 5 cm.
What is the total area of the bottom of all 6 paint cans? (Use = 3.14)
 
  (A)
(B)
(C)
(D)
(E)		 78.5 cm²
188.4 cm²
471 cm²
600 cm²
None of these. The answer is _________ cm².

 

Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
area, diameter, circles, squares
Description of task: 
Students use known diameters of tins to work out the floor area of a carton and a given number of tins.
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: 
   

Y9 (07/1997)

Y10 (07/1997)
a) C difficult moderate
b) C very difficult difficult
Diagnostic and formative information: 
  Student response Likely calculation Likely misconception
a) A 25 + 25 Confuses area (25 × 25) and perimeter (2 × (25 + 25)).
a) E – 156.25 12.52 Doesn't double the diameter before squaring.
b) E – 94.2 6r = 6 × 5 × Uses a perimeter calculation.