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

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 160cm2 in area. 80cm2 of blue glass and 80cm2 of clear glass.
How many panels are needed if the blue window glass used covers an area of 4.48m2?

I thought just convert 80cm2 into metres which I think is 80/100 = 0.8metres2. Then 4.48m2/0.8m2 = 5.6panels needed. The answer in the book says 560 panels needed.

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 160cm2 in area. 80cm2 of blue glass and 80cm2 of clear glass.
How many panels are needed if the blue window glass used covers an area of 4.48m2?

I thought just convert 80cm2 into metres which I think is 80/100 = 0.8metres2. Then 4.48m2/0.8m2 = 5.6panels needed. The answer in the book says 560 panels needed.

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

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

Guess what VOLUME conversion require?

Harry_the_cat

Full Member
1 metre = 100 cm

1 square metre = (100^2) square cm

1 cubic metre = (100^3) cubic cm

(Same for all the other conversions)