Question

Joseph has some strings that are all the same length. One string is the same length as the diameter of the circle below.

image

Joseph will use the strings to measure the circumference of the circle. How many strings will it take for him to measure around the circle exactly once?

A.
a little more than 2 strings

B.
a little more than 3 strings

C.
a little more than 4 strings

D.
a little more than 6 strings

Answer 1

To find out how many strings Joseph will need to measure the circumference of the circle, we can use the relationship between the circumference (C) and the diameter (D) of a circle, which is given by the formula:

\[
C = \pi D
\]

If the length of one string is equal to the length of the diameter of the circle (D), then we can express the circumference in terms of the string length.

Since one string covers the length of the diameter (D), the circumference (C) will be equal to:

\[
C = \pi \cdot D
\]

To find out how many strings he'll need, we can express it in terms of strings:

\[
\text{Number of strings} = \frac{C}{D} = \frac{\pi D}{D} = \pi
\]

The approximate value of \(\pi\) is about 3.14. Therefore, Joseph will need a little more than 3 strings to measure the circumference of the circle exactly once.

The correct answer is **B. a little more than 3 strings**.