Areas and Volumes (for Similar and non-similar figures)


(1) AREAs for Similar Figures

If figures are similar, the ratios of the lengths, widths and even perimeters are the same.
[Note: ratio can be seen as "scale factor".]


Similarity_1.jpg
http://www.nctm.org/standards/content.aspx?id=26770

Instructions

(a) Use the applet to show that the ratios of the lengths, widths and even perimeters are the same.
(b) Is the ratio of the LENGTHs the same as ratio of the AREAs?
i) Are the 2 ratios related?
ii) Do we need to find the actual areas (of both the figures) in order to find the ratio?

(2) AREAs and VOLUMEs for Similar Figures


Now that we know that
Mathsymbol_similarity_lengths_w_areas.jpg
We are going to explore the relationships between the ratios of (i) lengths, (ii)areas, and (iii) volumes.
Similarity_Volume.jpg
http://www.nctm.org/standards/content.aspx?id=25097

Instructions

(a) Use the applet to demonstrate how the ratios of the areas are related to the ratios of the volumes.
(b) Is there any relationship between the
(i) ratio of the lengths and (ii) ratio of the Areas
with ratio of the Volumes?

PAUSE ---- Still confused? Take a look at the below video:


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(3) Quiz Time!


Take 5 to 10 minutes to complete the following. Please include your class and index number under the name. (E.g. 2O314 Collin Tok)


End of Part 1

Please proceed to Part 2 (for non-Similar Figures).