Question

Ava draws a circle with radius 4 cm. Elliana draws a circle with diameter 6 cm. Without calculating, whose circle has the greater area? Explain.

Answer 1

Answer:

$\huge\boxed{\texttt{Ava\textsc{\char13}s circle}}$

Step-by-step explanation:

We can use the relationship between a radius and a diameter to find which circle has a greater area without calculating it.

We know that the diameter is twice the size of the radius.

• The diameter is the distance across the circle at the center
• The radius is the distance from the center of a circle to the edge

Using this, we can find the radius of a circle that has a diameter of 6.

Since the diameter is twice the radius, the radius will be half the diameter.

Since the diameter is 6, the radius is 3.

Circle areas can be calculated with the following formula, where r is the radius:

$\pi r^2$

Using this, we know that a higher value of r will get us a greater area. Therefore, we know that the greater value (3 or 4) will get us the greater area.

Since 4 is greater than 3, we know that the circle with the radius of 4 (Ava’s) will have a greater area.

Hope this helped!