Geoff wants to purchase a circular area rug for his room, but he can't decide between the small size and the large size. A small rug covers an area of approximately 67 square feet. If a large size rug has twice the dimensions of a small rug, how many times larger is the large rug?

Answer: The larger rug is 4 times larger

Step-by-step explanation:

The formula for determining the area of a circle is expressed as

Area = πr²

Where

r represents the radius of the circle.

π is a constant whose value is 3.14

The small circular rug covers an area of approximately 67 square feet. This means that

67 = πr²

r² = 67/π = 67/3.14 = 21.34

r = √21.34 = 4.62

If a large size rug has twice the dimensions of a small rug, it means that the radius of the larger rug would be

2 * 4.62 = 9.24

The area of the larger rug would be

3.14 * 9.24² = 268.06ft²

Therefore

268.06/67 = 4

The larger rug is 4 times larger