A device called an insolation metre is used to measure the intensity of sunlight. It has an area of 100 centimetres squared and registers 6.50 watts. What is the intensity in watts per metre squared?
Let’s start by highlighting some of the vital information given. We’re told that the metre has an area of 100 centimetres squared and that it registers a power reading of 6.50 watts. We want to know the intensity of sunlight; we’ll call that capital 𝐼. In particular, we want to solve for 𝐼 in units of watts per metre squared.
Our first step is to convert the area of 100 squared centimetres into metres squared. Recall that one centimetre is defined as 0.01 metres. That means if we multiply 100 centimetres squared by 0.01 metres divided by one centimetre, then all we are doing by multiplying it by this fraction is changing the units in which this number is expressed.
Our conversion factor right now is linear; it’s metres per centimetre, but the term we want to convert is squared in units of area. So let’s square our conversion factor too. When we distribute this square through the numerator and denominator of our conversion factor, it results in 0.01 squared metres squared divided by one centimetres squared. Now when we multiply our original area by this conversion factor, the centimetre squared terms cancel out, leaving us with a value in metres squared. And that value is 0.01 metres squared. This is the area of the metre in units of metres squared.
Going back to the original question, what is the intensity 𝐼? Intensity is equal to power divided by area. When we write this relationship for our scenario, the power is given in our problem statement as 6.50 watts and the area of the metre in units of metres squared is 0.01 metres squared. When we perform this division, we find a result for the intensity of 650 watts per metre squared. This is the intensity reading of the metre.