Question

A race track is in the form of a ring whose inner circumference is 352 m, and the outer circumference is 396 m. Find the width of the track and its area​

Answer 1

let the radius of inner track = r

2 pie r = 352

r = 56

let the radius of outer track = R

2 pie R = 396

R = 63

width of track = radius of outer track - radius of inner track

=63 - 56

= 7 m

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Answer 2

Let r1 and r2 be the radii of inner and outer Boundaries of the track

Inner circumference = 2πr1 = 352m

= $\sf{r1=\frac{352}{2π}m}$

Outer circumference = 2πr2

= $\sf{r2 = \frac{396}{2π}m}$

Width of the track = r2 - r1 =

$\sf{ \frac{1}{2\pi} \times (396 \times 352)m = \frac{7}{2 \times 22} \times 44 = 7m}$

Area of the track =

$\longrightarrow$$\sf{\pi( {r2}^{2} - {r1}^{2} )}$

$\longrightarrow$$\sf{\pi(r2 + r1)(r2 - r1)}$

$\longrightarrow$$\sf{\pi( \frac{396}{2\pi} + \frac{352}{2\pi} )}$

$\longrightarrow$$\sf{\pi \times \frac{748}{2\pi} \times {7m}^{2}}$

$\longrightarrow$$\sf{374 \times 7 {m}^{2}}$

$\longrightarrow$$\sf{2618 {m}^{2}}$