Question

a piece of land 120 ft by 240 ft contains a circular garden. surrounding the garden, there is a circular fence that is 20 ft in diameter. what is the area of the piece of land that is not part of the garden

Answer 1

the area of the piece of land that is not part of the garden is $28,486ft^2$ .

Step-by-step explanation:

Here we have , a piece of land 120 ft by 240 ft contains a circular garden. surrounding the garden, there is a circular fence that is 20 ft in diameter.  We need to find what is the area of the piece of land that is not part of the garden . Let's find out:

Let's calculate area of land and circular garden , and in order to find the area of the piece of land that is not part of the garden we will subtract area of circular garden from land !

Area of Land:

Area of land is given by

⇒ $length(width)$

⇒ $120(240)$

⇒ $28,880ft^2$

Area of Garden:

Area of circular garden given by

⇒ $\pi r^2$

⇒ $\pi (\frac{D}{2})^2$

⇒ $\pi (\frac{20}{2})^2$

⇒ $\pi (10)^2$

⇒ $100\pi$

⇒ $100(3.14)$

⇒ $314ft^2$

Hence , the area of the piece of land that is not part of the garden is 28,880-314 = 28,486 . Therefore , the area of the piece of land that is not part of the garden is $28,486ft^2$ .