Question

Zack has two circular clocks in his home, a small one in his kitchen and a larger one in his living room. If the small clock has a diameter of 8 inches, and the scale. factor from the small clock to the large clock is one to three, what is the area of the large clock?

Answer 1

The scale factor from the small clock to the large clock is 1:3, which means that the ratio of their diameters is 1:3.

Since the diameter of the small clock is 8 inches, the diameter of the large clock is:

3 * 8 = 24 inches

The area of a circle is given by the formula:

A = πr^2

where A is the area and r is the radius of the circle.

The radius of the large clock is half of its diameter, which is:

24 / 2 = 12 inches

Therefore, the area of the large clock is:

A = πr^2 = π(12)^2 = 144π

So the area of the large clock is 144π square inches