Question

what is the circumference of a circle with a diameter of 3.25 meters? estimate the circumference to the hundredths place using 3.14 for π. (1 point) 10.22 meters 10.2 meters 33.18 meters 10.21 meters

Explanation:

Step1: Recall the formula for the circumference of a circle

The formula for the circumference \( C \) of a circle when the diameter \( d \) is known is \( C=\pi d \).

Step2: Substitute the given values

We are given that \( d = 3.25 \) meters and \( \pi=3.14 \). Substituting these values into the formula, we get \( C = 3.14\times3.25 \).

Step3: Perform the multiplication

First, calculate \( 3.14\times3.25 \).
\( 3.14\times3.25=(3 + 0.14)\times(3+0.25)=3\times3+3\times0.25 + 0.14\times3+0.14\times0.25=9 + 0.75+0.42 + 0.035 = 10.205\approx10.21\) (when rounded to the hundredths place). Wait, let's do the multiplication directly: \( 3.25\times3.14 \).
\( 3.25\times3 = 9.75\), \( 3.25\times0.14=0.455\), then \( 9.75 + 0.455=10.205\approx10.21\)? Wait, maybe I made a mistake. Wait, \( 3.25\times3.14 \):

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Rounding \( 10.205 \) to the hundredths place: the thousandths digit is 5, so we round up the hundredths digit. \( 0 + 1=1 \), so \( 10.21 \)? But wait, let's check the options. The options are 10.22, 10.2, 33.18, 10.21. Wait, maybe my calculation is wrong. Wait, \( \pi d \), \( d = 3.25 \), \( \pi=3.14 \). \( 3.25\times3.14 \):

\( 3\times3.14 = 9.42 \), \( 0.25\times3.14=0.785 \), then \( 9.42+0.785 = 10.205 \), which is \( 10.21 \) when rounded to the hundredths place (since the third decimal is 5, we round the second decimal up: \( 0 + 1 = 1 \)). So the answer should be 10.21 meters? Wait, but let's check again. Wait, maybe the problem is that when multiplying \( 3.25\times3.14 \):

\( 3.25\times3.14=(3 + 0.25)\times3.14=3\times3.14+0.25\times3.14=9.42+0.785 = 10.205\), which is \( 10.21 \) when rounded to the hundredths place. So the correct option is 10.21 meters? Wait, but let's check the options. The options are:

• 10.22 meters

• 10.2 meters

• 33.18 meters

• 10.21 meters

So the answer is 10.21 meters. Wait, maybe I made a mistake in rounding? Wait, 10.205: the hundredths place is 0, thousandths is 5. So we round up the hundredths place: 0 becomes 1, so 10.21. So the correct option is 10.21 meters.

Answer:

10.21 meters