Question

an ice rink is being redesigned so that its radius is three times longer than before. how does this change affect the size of the rink? select one of four the circumference is nine times as large. the diameter is six times as large. the circumference will have tripled. the circumference is three times as large. remaining attempts: 1

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: Analyze the effect of changing the radius

Let the original radius be \(r_1\) and the new radius be \(r_2 = 3r_1\).
The original circumference \(C_1=2\pi r_1\).
The new circumference \(C_2 = 2\pi r_2=2\pi(3r_1) = 3\times(2\pi r_1)=3C_1\).

Step3: Recall the formula for diameter

The formula for the diameter of a circle is \(d = 2r\). If the radius is tripled (\(r_2 = 3r_1\)), then the new diameter \(d_2=2r_2 = 2\times(3r_1)=3d_1\) (not six - times).

Answer:

The circumference is three times as large.