Question

A track is in the form of a ring whose inner circumference is 352 m and the outer circumference is 396 m. The width of the track is

• A. 44m
• B. 14m
• C. 22m
• D. 7m

Answer 1

The Correct Option is D

The correct option is (D): 7m
We are given the inner and outer circumferences of a ring-shaped track. To find the width of the track, we can use the relationship between the circumference and the radius of a circle.

Step 1: Formula for Circumference
The formula for the circumference of a circle is:
\[C = 2 \pi r\]
where \(C\) is the circumference and \(r\) is the radius.

Step 2: Find the inner and outer radii
We can use the circumferences to find the corresponding radii.

1. Inner radius \(r_{\text{inner}}\):
\[C_{\text{inner}} = 2 \pi r_{\text{inner}} = 352 \, \text{m}\]
Solving for \(r_{\text{inner}}\):
\[r_{\text{inner}} = \frac{352}{2 \pi} = \frac{352}{6.28} \approx 56 \, \text{m}\]

2. **Outer radius** \(r_{\text{outer}}\):
\[C_{\text{outer}} = 2 \pi r_{\text{outer}} = 396 \, \text{m}\]
Solving for \(r_{\text{outer}}\):
\[r_{\text{outer}} = \frac{396}{2 \pi} = \frac{396}{6.28} \approx 63 \, \text{m}\]

Step 3: Calculate the width of the track
The width of the track is the difference between the outer and inner radii:
\[\text{Width} = r_{\text{outer}} - r_{\text{inner}} = 63 \, \text{m} - 56 \, \text{m} = 7 \, \text{m}\]

Final Answer:
The width of the track is 7 meters.