Question

A racetrack is in the form of a ring whose inner and outer circumference are 437 and 503, respectively. Find the width of the track and also its area

Answer 1

Question:

A racetrack is in the form of a ring whose inner and outer circumference are 437 and 503, respectively. Find the width of the track and also its area.

Given:

A racetrack is in the form of a ring

• Inner Circumference: 437

• Outer Circumference: 503

To Find:

• Width

• Area

Solution:

Calculating Inner Radius:

We know that,

• Inner circumference = 437m

Now,

$437 = 2 πr \\ \\ 437 = 2 \times \frac{22}{7}r \: \\ \\ r = \frac{437 \times 7}{2 \times 22} \\ \\ r= 69.522$

Inner radius = 69.522 m

Calculating Outer Radius:

We know that,

• Outer circumference = 503m

Now,

$503 = 2πr \\ \\ 503 = 2 \times \frac{22}{7} r \\ \\ r = \frac{503 \times 7}{2 \times 22} \\ \\ r \: = 80.022m$

Outer radius = 80.022 m

Calculating Width of track:

• Width of track = Outer radius - Inner radius

= 80.022 m - 69.522 m

= 10.5 m

Calculating Area of the Track:

• Area of track = Outer area - inner area

$= π {R}^{2} - π \: {r}^{2}$

$=\ π\:(R^2 -r^2)$

$=\frac{22}{7} \times (80.022^2 -69.522^2)$

$=\:4934.952 m^2$

Therefore,

• Width of the track  is 10.5 m

• Area of the track is 4934.952m²

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