A circle has a radius of centimeters. What is the area of the circle, in square centimeters, in terms of ?
For circle area problems, immediately recall and write down the formula , then carefully identify whether the given value is a radius or a diameter (if it is a diameter, divide by 2 first). Substitute the radius, square it—don’t just double it—and then attach as a factor. Finally, match your simplified expression (like ) directly to the given answer choices without overcomputing the decimal value.
Hints
Identify the correct formula
You are asked for the area of a circle. Which formula involves and the radius (not the diameter)?
Use the given radius
Once you have the formula, plug in the radius . Be careful not to confuse the radius with the diameter.
Handle the exponent correctly
The radius is squared in the formula. What is ? After finding that, multiply the result by .
Desmos Guide
Use Desmos to verify the calculation
In the expression line, type pi*(4^2) and press Enter. The output value that Desmos shows is the numerical value of the circle’s area; match this value to the choice written with in the answer options.
Step-by-step Explanation
Recall the area formula for a circle
The area of a circle with radius is given by the formula
This means you take the radius, square it, and then multiply by .
Substitute the given radius
The problem says the radius is centimeters, so substitute into the formula:
Now you just need to simplify .
Square the radius and simplify the expression
Compute :
So the area becomes , which is square centimeters. Therefore, the correct answer choice is .