The diagram shows a quarter circle which has a radius of 10 centimeters. Calculate the area of this quarter circle, giving your answer in terms of 𝜋.
The area of any circle can be calculated using the formula 𝜋𝑟 squared, multiplying the radius squared by 𝜋. We can therefore work out the area of a quarter circle by finding a quarter of 𝜋𝑟 squared or 𝜋𝑟 squared divided by four as finding a quarter is the same as dividing by four. The radius of our quarter circle is 10 centimeters. Therefore, we can calculate the area by multiplying 10 squared by 𝜋 and then dividing by four.
Squaring a number means multiplying it by itself. Therefore, 10 squared is equal to 10 multiplied by 10. This is equal to 100. The area is equal to 𝜋 multiplied by 100 divided by four. 𝜋 multiplied by 100 can be written as 100𝜋. As we were told to give our answer in terms of 𝜋, we know there must be a 𝜋 in the answer. Our final step is to divide 100𝜋 by four or find a quarter of 100𝜋. One-quarter of 100 is equal to 25. We know that one-half of 100 is 50. Halving this again gives us 25. This means that 100𝜋 divided by four is equal to 25𝜋.
The area of the quarter circle in terms of 𝜋 is 25𝜋 centimeters squared. Note that any time we’re calculating an area, our units are squared, centimetre squared, metre squared, et cetera.