Question

Find the area and the circumference of a circle with diameter 9 yd.Use the value 3.14 for pi, and do not round your answers. Be sure to include the correct units in your answers.

Answer 1

Area and circumference of a circle

area = 63.585 yd²

circumference = 28.26 yd

Step-by-step explanation

Radius

Since the diameter of a circle is twice its radius, then the radius of this circle is half 9 yd:

radius = diameter ÷2

= 9 yd÷2 = 4.5 yd

The radius of this circle is 4.5 yd.

Area

The area of a circle is given by the equation:

`area=\pi r^2`

where r is the radius, then in this case:

`\begin{gathered} area=\pi(4.5yd)^2 \\ \end{gathered}`

Using π = 3.14

`\begin{gathered} area=3.14\cdot(4.5yd)^2 \\ =3.14\cdot(4.5)^2yd^2 \\ =63.585yd^(2) \end{gathered}`

Then, the area of this circle is 63.585 yd².

Perimeter

The perimeter of a circle is given by:

`perimeter=2\pi r`

where r is the radius, then:

`perimeter=2\pi\cdot4.5yd`