How many square centimeters is a square meter?

[Haibara Ai]

How many square centimeters is a square meter, and how many square meters a square kilometer? thanks

 

[Mentallic]

There is an easy way to figure out these problems, but its pointless if you don't understand the reasoning behind it.

Take a metre, and square it to have a metre squared. Now realize that 1 metre = 100 centimetres by definition. This means you can fit 100 centimetres along the metre-squared's length, and 100 centimetres along the metre-squared's width. Now, you should know that the area = length * breadth. So area = 100cm * 100cm = 10,000cm²

Thus, 1m²=10,000cm²=100²cm²

As for the square kilometre. There are 1000 metres in 1km. So if we take 1km², we can fit 1000m along the length, and 1000m along the width. Area=1000m*1000m=1,000,000m²

Thus, 1km²=1000²m²=10¹⁰cm²


Similarly, you can do this for volumes.

e.g. 1m³ is how many cm³? Well, 100cm=1m, and volume = length * breadth * height = 100cm*100cm*100cm = 1,000,000cm³=10⁶cm³

In summary ~ For area, to find the amount of m² to km² or cm² to mm² etc. Just realize how many of those units are equal to the other larger/smaller metric unit, and square it. For volumes, cube it.

 

[Haibara Ai]

Ok, thanks a lot

 

[bobmerhebi]

Hello, can anyone tell me why is the area of a wire pi (r/2)^2 & not that of a cylinder 2pi.rl ? thx

 

[HallsofIvy]

$2\pi r l$ is the area of the curved surface of a cylinder of radius r and length l. It does not include the area of the two circular bases.

And in the future, remember that it is better to start your own thread than add a new question onto another person's.

 

[LowlyPion]

Hello, can anyone tell me why is the area of a wire pi (r/2)^2 & not that of a cylinder 2pi.rl ? thx

Are you asking about the cross sectional area of the wire which is π(d/2)² since wire gauges are usually given as diameters?

Or as Halls of Ivy has asked if you wanted the area of the entire radial surface of the wire without the cross sections?