Question

Aisha measured a round jar lid. Then she calculated that the circumference of the lid is 18.84 centimeters. What is the lid's area?

Answer 1

lid's area is approximately 28.2457 square centimeters.

Explanation:

The formula to calculate the circumference of a circle is:

`\sf Circumference = 2 * \pi * Radius`

Given that the circumference is 18.84 centimeters, we can solve for the radius:

`\begin{aligned} & \sf 18.84 = 2 * pi * Radius\\\\&\textsf{Now, isolate the radius:}\\\\& \sf Radius = (18.84 )/( (2 * \pi)) \\ \\ \end{aligned}`

Now that we have the radius, we can use it to calculate the area of the circle.

The formula for the area of a circle is:

`\sf Area = \pi * Radius^2`

Substitute the value of the radius:

`\sf Area = \pi * \left((18.84 )/( (2 * \pi))\right)^2`

Simplify:

`\sf Area = \pi * \left((9.42)/(\pi)\right)^2`

`\sf Area =( (\pi * 88.7364) )/(\pi^2)`

`\sf Area =( ( 88.7364) )/(\pi)`

Using the value of π (approximately 3.14159):

`\sf Area =( ( 88.7364) )/(3.14159)`

`\sf Area \approx 28.2457 cm^2`

So, the lid's area is approximately 28.2457 square centimeters.