Question

1. the distance around a meteor crater is 9,687 feet. find the diameter of the crater. use \\(\frac{22}{7}\\) for \\(\pi\\). round to the nearest tenth.

Explanation:

Step1: Recall the formula for the circumference of a circle

The formula for the circumference \( C \) of a circle is \( C=\pi d \), where \( d \) is the diameter. We know \( C = 9687 \) feet and \( \pi=\frac{22}{7} \). We need to solve for \( d \), so we can rearrange the formula to \( d=\frac{C}{\pi} \).

Step2: Substitute the values into the formula

Substitute \( C = 9687 \) and \( \pi=\frac{22}{7} \) into the formula for \( d \). So \( d=\frac{9687}{\frac{22}{7}} \). When dividing by a fraction, we multiply by its reciprocal, so \( d = 9687\times\frac{7}{22} \).

Step3: Calculate the product

First, calculate \( 9687\times7 = 67809 \). Then divide by 22: \( \frac{67809}{22}=3082.227\cdots \)

Step4: Round to the nearest tenth

The number \( 3082.227\cdots \) rounded to the nearest tenth is \( 3082.2 \) (since the hundredth digit is 2, which is less than 5, we keep the tenth digit as it is).

Answer:

The diameter of the crater is \( 3082.2 \) feet.