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How many of X to fill a space of X metres squared?

badatmath

New member
Hi, so I've started doing what I think is geometry.. ^^' and stumbling at this first practical question...

A panel of clear and blue glass is 160cm[SUP]2 [/SUP]in area. 80cm[SUP]2[/SUP] of blue glass and 80cm[SUP]2 [/SUP]of clear glass.
How many panels are needed if the blue window glass used covers an area of 4.48m[SUP]2[/SUP]?

I thought just convert 80cm[SUP]2[/SUP] into metres which I think is 80/100 = 0.8metres[SUP]2[/SUP]. Then 4.48m[SUP]2[/SUP]/0.8m[SUP]2[/SUP] = 5.6panels needed. The answer in the book says 560 panels needed.
Please help and thank you.
 

tkhunny

Moderator
Staff member
Hi, so I've started doing what I think is geometry.. ^^' and stumbling at this first practical question...

A panel of clear and blue glass is 160cm[SUP]2 [/SUP]in area. 80cm[SUP]2[/SUP] of blue glass and 80cm[SUP]2 [/SUP]of clear glass.
How many panels are needed if the blue window glass used covers an area of 4.48m[SUP]2[/SUP]?

I thought just convert 80cm[SUP]2[/SUP] into metres which I think is 80/100 = 0.8metres[SUP]2[/SUP]. Then 4.48m[SUP]2[/SUP]/0.8m[SUP]2[/SUP] = 5.6panels needed. The answer in the book says 560 panels needed.
Please help and thank you.

Careful with your conversions.

\(\displaystyle 80\;cm^2\cdot \left(\dfrac{1\;m}{100\;cm}\right)^{2} = \dfrac{80}{100^{2}}\;m^2 \ne 0.8\;m^2\)

AREA conversions require SQUARED conversion factors. One cannot convert just one direction.

Guess what VOLUME conversion require?
 
1 metre = 100 cm

1 square metre = (100^2) square cm

1 cubic metre = (100^3) cubic cm

(Same for all the other conversions)
 
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