Question

a circle has a radius of 2.5 cm. which of the following would be the diameter of the same circle?
a 4.0 cm
b 4.5 cm
c 5.0 cm
d 5.5 cm
question #3
select all of the statements that are not true about circles.
a the circumference is about 2 times the diameter.
b the radius is half of the diameter.
c the radius divides a circle in half.
d the diameter is half of the radius.
e a chord must go through the center of a circle.
f the diameter is a chord.
question #4
identify each representation that is an approximation for pi.
a 1.34
b \\(\frac{4}{9}\\)
c \\(\frac{7}{22}\\)
d \\(d + c\\)
e 3.14
f \\(\frac{22}{7}\\)

Explanation:

Question 1 (Diameter of a circle)

Step1: Recall the formula for diameter

The diameter \( d \) of a circle is related to the radius \( r \) by the formula \( d = 2r \).

Step2: Substitute the given radius

Given \( r = 2.5 \) cm, substitute into the formula: \( d = 2\times2.5 \)

Step3: Calculate the diameter

\( 2\times2.5 = 5.0 \) cm.

• Option A: Circumference \( C=\pi d\approx3.14d \), not about 2 times \( d \), so A is not true.
• Option B: Radius \( r = \frac{d}{2} \), so B is true.
• Option C: A radius is a line from center to edge; a diameter (2 radii) divides the circle in half, not a single radius, so C is not true.
• Option D: Diameter \( d = 2r \), not half of \( r \), so D is not true.
• Option E: A chord is a line segment with endpoints on the circle; only the diameter (a special chord) goes through the center, so E is not true.
• Option F: Diameter is a chord (since it has endpoints on the circle and passes through center), so F is true.

Step1: Recall \( \pi \) value

\( \pi\approx3.14\approx\frac{22}{7}\approx3.14159\).

Step2: Analyze each option

• Option A: 1.34 is not close to \( \pi \), so no.
• Option B: \( \frac{5}{8}=0.625 \), not close, so no.
• Option C: \( \frac{7}{22}\approx0.318 \), not close, so no.
• Option D: \( d + c \) is a sum of diameter and circumference, not an approximation for \( \pi \), so no.
• Option E: 3.14 is a common approximation for \( \pi \), so yes.
• Option F: \( \frac{22}{7}\approx3.1429 \), which is an approximation for \( \pi \), so yes.

Answer:

C. 5.0 cm

Question 3 (Statements NOT true about circles)