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` .

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 ((D)/(2))^2`

⇒
`\pi ((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` .