Cylinders with the same volume

Cylinders with the same volume

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about working out the height of two cylinder shapes given the volume and the radius.

Question 1Change answer

The two cylinders below each contain 226 cm3 of liquid.

two cylinder shapes

What is the height of each cylinder if the measurements are as shown?
Use = 3.14 approx.

a)  Height of P :  cm
b)  Height of Q :  cm

Question

The two cylinders below each contain 226 cm3 of liquid.

c)  If the height of P was 5 cm and the height of Q was 20 cm, which statement below would be correct about the radius of each cylinder, if the volume was the same?

    • (A) Radius of P is the same as the radius of Q.

    • (B) Radius of P is half the radius of Q.

    • (C) Radius of P is twice the radius of Q.

    • (D) Radius of P is four times the radius of Q.

    • (E) Nothing definite can be said without more information.

Task administration: 
This task can be completed with pencil and paper or online.
Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
volume, cylinders, circumference, radius
Description of task: 
Students calculate the height of two cylinders given the radius, and identify a correct general statement about the relationship between radius and height for a given 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: 
 

Y9 (10/1996)
a) Height of P is 2 (226 ÷ (3.14 × 6 × 6))
[Accept answers between 1.99 and 2.]		 very difficult
b) Height of Q is 8 (226 ÷ (3.14 × 3 × 3))
[Accept answers between 7.98 and 8.]		 very difficult
c) (C) Radius of P is twice the radius of Q. difficult