To find out how much greater the circumference of the outer circle is compared to the inner circle, we first need to find the radii of both circles.
-
Find the radius of the inner circle: The formula for the circumference \( C \) of a circle is given by:
\[ C = 2\pi r \]
Given that the circumference of the inner circle is 88 ft, we can set up the equation:
\[ 88 = 2 \times \frac{22}{7} \times r_{inner} \]
To find \( r_{inner} \), we can rearrange this equation:
\[ r_{inner} = \frac{88}{2 \times \frac{22}{7}} = \frac{88 \times 7}{2 \times 22} = \frac{88 \times 7}{44} = 14 \text{ ft} \]
-
Find the radius of the outer circle: The distance between the inner circle and the outer circle is 4 ft, so the radius of the outer circle is:
\[ r_{outer} = r_{inner} + 4 = 14 + 4 = 18 \text{ ft} \]
-
Calculate the circumference of the outer circle: Using the same formula for circumference:
\[ C_{outer} = 2\pi r_{outer} = 2 \times \frac{22}{7} \times 18 \]
Calculating this gives:
\[ C_{outer} = 2 \times \frac{22}{7} \times 18 = \frac{22 \times 36}{7} = \frac{792}{7} \approx 113.14 \text{ ft} \]
-
Calculate the difference in circumference: Now, we subtract the circumference of the inner circle from that of the outer circle.
\[ \text{Difference} = C_{outer} - C_{inner} = \frac{792}{7} - 88 \]
Convert 88 to a fraction with a denominator of 7:
\[ 88 = \frac{88 \times 7}{7} = \frac{616}{7} \]
Now compute the difference:
\[ \text{Difference} = \frac{792}{7} - \frac{616}{7} = \frac{792 - 616}{7} = \frac{176}{7} \approx 25.14 \text{ ft} \]
-
Round to the nearest tenth: Rounding 25.14 ft to the nearest tenth gives:
\[ 25.1 \text{ ft} \]
Thus, the circumference of the outer circle is approximately 25.1 ft greater than the circumference of the inner circle.