What is a larger area 160 square inches or a circle with a 47cm diameter and by how much?

Answer 1

For this problem we want to compare the areas of two things.

One of them is given, 160 sq inches. We know that it's area because they tell us and it's also in units squared (which is characteristic of area).

To compare, we should calculate the area of a circle.

It is common knowledge that the area of a circle is A = 2pi(r) where pi is the constant 3.14 and r is the radius.

We are given diameter. 1/2 d = r, so 1/2 (47) = r.

However, the dimensions of the larger area are in inches, so we want to convert chm into inches so we can be consistent and compare within the same units.

47 cm = 0.47 m. 1 meter has 39.37 inches.

So 0.47 m * (39.37 inches/1meter) = 18.5 inches.

This is diameter. As I said above, half of that is radius --> 9.25.

Now we can evaluate Area.

A=2 pi r = 2 (3.14) (9.25) = 58 inches squared.

The other area is larger by 160-58 = 102 inches squared.