Question

what is the circumference of a circle with a diameter of 3.75 kilometers? estimate the circumference to the hundredths place using 3.14 as π. (1 point)
11.78 kilometers
12 kilometers
44.18 kilometers
11.79 kilometers

Explanation:

Step1: Recall the formula for the circumference of a circle

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

Step2: Substitute the given values into the formula

We are given that \( d = 3.75 \) kilometers and \( \pi=3.14 \). Substituting these values into the formula, we get \( C = 3.14\times3.75 \).

Step3: Perform the multiplication

First, calculate \( 3.14\times3.75 \).

$$
LATEXBLOCK0
$$

Step4: Round to the hundredths place

To round \( 11.775 \) to the hundredths place, we look at the thousandths digit, which is 5. When the thousandths digit is 5 or greater, we round up the hundredths digit. So, \( 11.775\approx11.78 \) (wait, no, wait: \( 11.775 \) rounded to the hundredths place: the hundredths digit is 7, the thousandths is 5, so we add 1 to the hundredths digit: \( 7 + 1=8 \)? Wait, no, \( 11.775 \): the number is \( 11.775 \), so the tenths place is 7, hundredths is 7, thousandths is 5. Rounding to the hundredths place, we take the first two decimal places and look at the third. Since the third is 5, we round the second decimal place up. So \( 11.775\approx11.78 \)? Wait, no, wait, \( 3.14\times3.75 = 11.775 \), and when rounding to the hundredths place, we check the thousandths digit (5). So we round the hundredths digit (7) up by 1, so \( 7+1 = 8 \), so the number is \( 11.78 \)? Wait, but let's recalculate \( 3.14\times3.75 \) directly:

\( 3.75\times3 = 11.25 \), \( 3.75\times0.14=0.525 \), and \( 11.25 + 0.525=11.775 \). Now, rounding \( 11.775 \) to the hundredths place: the rule is that if the digit in the thousandths place is 5 or more, we round up the hundredths place. So \( 11.775 \) rounded to the hundredths place is \( 11.78 \)? Wait, no, \( 11.775 \) is exactly halfway between \( 11.77 \) and \( 11.78 \), but the standard rounding rule for 5 is to round up. Wait, but let's check the multiplication again. Wait, \( 3.14\times3.75 \):

\( 3.75\times3 = 11.25 \)

\( 3.75\times0.1 = 0.375 \)

\( 3.75\times0.04=0.15 \)

So \( 0.375 + 0.15=0.525 \), then \( 11.25+0.525 = 11.775 \). Now, rounding to the hundredths place: the number is \( 11.775 \), so the hundredths digit is 7, the next digit is 5, so we round the 7 up to 8, so \( 11.78 \). Wait, but wait, the options have 11.78 and 11.79. Wait, maybe I made a mistake. Wait, no, \( 3.14\times3.75 = 11.775 \), which is 11.78 when rounded to the hundredths place (because the third decimal is 5, so we round the second decimal up: 7 becomes 8). Wait, but let's check with a calculator: 3.14 3.75. 3.75 3 = 11.25, 3.75 0.14 = 0.525, 11.25 + 0.525 = 11.775. So 11.775 rounded to the hundredths place is 11.78 (since the thousandths digit is 5, we round the hundredths digit 7 up to 8). Wait, but the option is 11.78 kilometers. Wait, but let me check again. Wait, 3.14 3.75:

3.14
x3.75
------
1570
21980
94200
------
117750
So moving the decimal three places (since 3.14 has two decimal places and 3.75 has two, total four? Wait, no, 3.14 is two decimal places, 3.75 is two decimal places, so the product has 2 + 2 = 4 decimal places? Wait, no, 3.14 3.75: 314 375 = 117750, then we have four decimal places? Wait, no, 3.14 is 314/100, 3.75 is 375/100, so (314375)/(100100)=117750/10000 = 11.775. So 11.775 is the exact value. Rounding to the hundredths place: look at the thousandths digit, which is 5. So we round the hundredths digit (7) up by 1, so 7 + 1 = 8, so 11.78. So the correct answer is 11.78 kilometers.

Answer:

11.78 kilometers