Question

A landscaper is building two circular gardens. The smaller garden has a radius of 2 meters. The larger garden has an area that is 7 times greater than the smaller garden. Approximately how much greater is the area of the larger garden than the area of the smaller garden?

Answer 1

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.