Question

select all the statements that are true.
the radius of a circle is twice its diameter.
to find the diameter of a circle, divide its circumference by $pi$.
the circumference of a circle is greater than its diameter.
the circumference of a circle is twice its radius.
the circumference divided by the diameter is $pi$

Explanation:

1. Analyze the first statement: The radius of a circle is half its diameter (since \(d = 2r\) or \(r=\frac{d}{2}\)), so "The radius of a circle is twice its diameter" is false.
2. Analyze the second statement: The formula for the circumference of a circle is \(C=\pi d\). Solving for \(d\), we get \(d = \frac{C}{\pi}\). So "To find the diameter of a circle, divide its circumference by \(\pi\)" is true.
3. Analyze the third statement: Since \(C=\pi d\) and \(\pi\approx3.14> 1\), \(C=\pi d>d\) (when \(d>0\)). So "The circumference of a circle is greater than its diameter" is true.
4. Analyze the fourth statement: The formula for the circumference of a circle is \(C = 2\pi r\), which means the circumference is \(2\pi\) times the radius, not twice the radius. So "The circumference of a circle is twice its radius" is false.
5. Analyze the fifth statement: From \(C=\pi d\), dividing both sides by \(d\) (where \(d

eq0\)) gives \(\frac{C}{d}=\pi\). So "The circumference divided by the diameter is \(\pi\)" is true.

Answer:

• To find the diameter of a circle, divide its circumference by \(\pi\).
• The circumference of a circle is greater than its diameter.
• The circumference divided by the diameter is \(\pi\)