Jenna is planting four circular gardens. She is planting one garden each for tomatoes, carrots, cabbage, and strawberries. Each garden will have a fence around it to keep rabbits out. The tomato, carrot, and cabbage gardens will all be the same size. Since Jenna loves strawberries, the strawberry garden will be larger. It will use the same amount of fencing as the other three gardens combined. She used a total of about 113.04 feet of fencing material.

Question

Jenna is planting four circular gardens. She is planting one garden each for tomatoes, carrots, cabbage, and strawberries. Each garden will have a fence around it to keep rabbits out. The tomato, carrot, and cabbage gardens will all be the same size. Since Jenna loves strawberries, the strawberry garden will be larger. It will use the same amount of fencing as the other three gardens combined. She used a total of about 113.04 feet of fencing material.

The area of the each smaller garden is about ___ square feet.

The area of the larger garden is about ___ square feet.

The area of the larger garden is ____ times larger than the area of the smaller garden.

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Answer 1

Bot GPT 3.5 answered

The total length of fencing material used is 113.04 feet. Since the tomato, carrot, and cabbage gardens are all the same size, each of those gardens used 113.04 feet / 4 = 28.26 feet of fencing material.

Each smaller garden has a circumference of 28.26 feet, so the radius of each smaller garden is 28.26 feet / (2 * π) = 4.5 feet. Therefore, the area of each smaller garden is π * (4.5)^2 = 63.59 square feet.

The strawberry garden uses the same amount of fencing as the other three gardens combined, so it used 3 * 28.26 = 84.78 feet of fencing material. The radius of the strawberry garden is 84.78 feet / (2 * π) = 13.5 feet. Therefore, the area of the larger garden is π * (13.5)^2 = 572.55 square feet.

The area of the larger garden is 572.55 / 63.59 = 9 times larger than the area of each smaller garden.