Answer:75.36 square meters
The area of the smaller garden can be calculated using the formula for the area of a circle:
A = πr^2
where r is the radius of the circle. Substituting r = 2 meters, we get:
A(smaller) = π(2)^2 = 4π
The area of the larger garden is 7 times greater than the area of the smaller garden. Therefore, the area of the larger garden can be found by multiplying the area of the smaller garden by 7:
A(larger) = 7A(smaller) = 7(4π) = 28π
To find how much greater the area of the larger garden is than the area of the smaller garden, we can subtract the area of the smaller garden from the area of the larger garden:
A(larger) - A(smaller) = 28π - 4π = 24π
So, the area of the larger garden is approximately 24π square meters greater than the area of the smaller garden.
To get a decimal approximation, we can use the value of π as 3.14:
A(larger) - A(smaller) ≈ 24(3.14) ≈ 75.36
Therefore, the area of the larger garden is approximately 75.36 square meters greater than the area of the smaller garden.