Question

fluency and skills practice | name lesson 6 using the relationship between a circles circumference and diameter continued what is the circumference of a circle with radius 64 inches? write your answer using π a circle has circumference 20π feet. what is the radius of the circle? some answers use 3.14 for π, and some answers use the symbol π in the solution. which type of answer is more accurate? explain. grade 7 • lesson 6

Explanation:

Step1: Recall the formula for circumference

The formula for the circumference of a circle is $C = 2\pi r$, where $r$ is the radius.

Step2: Calculate the circumference for the first - part

Given $r = 94$ inches, substituting into the formula $C = 2\pi r$, we get $C=2\pi\times94 = 188\pi$ inches.

Step3: Recall the formula for circumference to find radius

The formula for the circumference of a circle is $C = 2\pi r$. We can solve for $r$ when $C = 20\pi$ feet. Rearranging the formula gives $r=\frac{C}{2\pi}$.

Step4: Calculate the radius for the second - part

Substituting $C = 20\pi$ into $r=\frac{C}{2\pi}$, we have $r=\frac{20\pi}{2\pi}=10$ feet.

Step5: Analyze accuracy of $\pi$ representations

$\pi$ is an irrational number with an infinite non - repeating decimal expansion ($\pi=3.1415926535\cdots$). Using the symbol $\pi$ in the answer is more accurate because 3.14 is only an approximation of $\pi$. When we use 3.14, we introduce a rounding error.

Answer:

1. The circumference of the circle with radius 94 inches is $188\pi$ inches.
2. The radius of the circle with circumference $20\pi$ feet is 10 feet.
3. Using the symbol $\pi$ in the answer is more accurate because 3.14 is only an approximation of $\pi$ and using it introduces a rounding error.