Question

try it! what is the circumference of the rim of a basketball hoop with a radius of 9 inches?
first, multiply the radius by $square$ to get the diameter, $square$ inches.
then, multiply the diameter by 3.14 (an approximation for $pi$) to get a circumference of about $square$ inches.
convince me! if the diameter is doubled, what happens to the circumference? explain.
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listen actively as others share ideas.

Explanation:

Step1: Find diameter from radius

$d = 2 \times r = 2 \times 9 = 18$ inches

Step2: Calculate circumference

$C = \pi \times d = 3.14 \times 18 = 56.52$ inches

Step3: Analyze doubled diameter effect

Original diameter $d_1=18$, new diameter $d_2=2\times18=36$. New circumference $C_2=3.14\times36=113.04$. $\frac{C_2}{C_1}=\frac{113.04}{56.52}=2$, so circumference doubles.

Answer:

First blank: 2, second blank: 18, third blank: 56.52
When the diameter is doubled, the circumference also doubles, because circumference is directly proportional to diameter ($C=\pi d$), so doubling the diameter multiplies the circumference by 2.