Questions: Relating Area to Circumference Leo is staining a circular table. It has a circumference of 69 inches. What is its approximate area? You're trying to find the area of a circle, but you are given the circumference. Which is a formula for circumference? C=69 C=πd C=πr C=πr^2

Relating Area to Circumference

Leo is staining a circular table. It has a circumference of 69 inches. What is its approximate area?

You're trying to find the area of a circle, but you are given the circumference. Which is a formula for circumference?
C=69
C=πd
C=πr
C=πr^2

Transcript text: Relating Area to Circumference Leo is staining a circular table. It has a circumference of 69 inches. What is its approximate area? You're trying to find the area of a circle, but you are given the circumference. Which is a formula for circumference? \[ C=69 \] $C=\pi d$ $C=\pi r$ $C=\pi r^{2}$

Solution

Solution Steps

Step 1: Find the radius

The formula for the circumference of a circle is given by _C_ = 2π_r_, where _r_ is the radius. We are given that the circumference is 69 inches. So, we can set up the equation:

69 = 2π_r_

Solving for _r_, we get:

_r_ = 69 / (2π) ≈ 10.97 inches

Step 2: Calculate the area

The formula for the area of a circle is _A_ = π_r_². Now that we have the approximate value of the radius, we can substitute it into the area formula:

_A_ = π * (10.97)²

Step 3: Compute the area

_A_ ≈ π * 120.34 ≈ 378.04 square inches