Blocks and a cylinder

Blocks and a cylinder

Pencil and paper
Overview
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about calculating the volume of blocks in a cylinder.
Anaru packed three blocks into a cylinder, one block on top of the other.

a)
Find the total volume of the three blocks each measuring 4 cm × 3 cm × 3 cm.
 
__________ cm³
 
b)
Find the volume of the cylinder which has a diameter of 5 cm and a height of 9 cm. 
(Take = 3.14)
 
__________ cm³
 
c) How much empty space is left around the blocks? __________ cm³

  Show any working here

 

 

Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
volume, cuboids, 3-dimensional shapes, cylinders
Description of task: 
Students calculate the volume of blocks in a cylinder, the cylinder and the space around the blocks.
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 (07/97)

Y10 (07/97)
a) 108 ((4 × 3 × 3) × 3) moderate moderate
b) 176.625 ((3.14 × 2.5²) × 9)
[Accept 176.6 – 176.8]		 very difficult very difficult
c) 68.625 [Accept 68.6 – 68.8]
NOTE: This mark can be obtained by correct subtraction of b) - a) even if incorrect answer obtained in a) or b).		 difficult difficult
Diagnostic and formative information: 
  Student response Likely calculation Likely misconception
a) 36 
324 		 4 × 3 × 3
(4 × 3 × 3) × 9		 Volume of one block only.
Volume of nine blocks. Interpret 9 cm height as nine blocks.
b) 141.3 (approx.) (3.14 × 5) × 9 Uses d for area rather than r².