Question

5) Circle A has a radius of 5in Circle B has a diameter of 16. Which circlehas a larger area? (draw out the question belowA) Circle A's area is 39s in greater than Circle B's areaB Circle A's area is 22 in greater than Circle B's areaC) Circle B's area is 39 in greater than Circle A's areaD) Circle B's area is 256 in greater than Circle A's area

Answer 1

The area of a circle is directly proportional to its diameter or radius, which means the larger the diameter/radius is, the larger will the area be.

In this case, Circle A has 5 inches of radius, and Circle B has 16 inches of diameter, but the radius is half the diameter, so Circle B actually has 8 inches of the radius.

Given that Circle B has a larger radius, we can deduct that it has a larger area.

Let's find each area.

$\begin{gathered} A_a=\pi(5)^2=25\pi \\ A_b=\pi(8)^2=64\pi \end{gathered}$

If we subtract, we find that Circle B is 39 square inches greater than Circle A.

Hence, the answer is C.