Question

the inner and outer circumference of a track are 154 m and 266m find the width of the track​

Answer 1

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Given:

Inner circumference = 154 m

Outer circumference = 266 m

To find:

Width of track = ?

Solution:

Refer attachment for more elaboration

Let radius of inner circumference be r and outer circumference be R

Note: If we have to find the width we have to first find length of radius of inner and outer circumference then we will subtract the outer circumference radius with inner to find width

$\\ \\ circumference \: = 2\pi \: r \\ \\ For \: inner \: radius \\ \\ circumference = 2\pi \: r \\ \\ 154 = 2\pi \: r$

$\\ \\ \dfrac{154}{2\pi} = r \\ \\ \dfrac{77}{\pi} = r \\ \\ For \: outer \: radius \\ \\ circumference = 2\pi \:R$

$\\ \\ 266 = 2\pi \: R \\ \\ \dfrac{266}{2\pi} = R \\ \\ \dfrac{133}{\pi} = R$

$\\ \\ Width = R - r \\ \\ Width = \dfrac{133}{\pi} - \dfrac{77}{\pi} \\ \\ Width = \dfrac{56}{\pi} \\ \\ Width = \dfrac{56}{3.14} = 17.8 \: m$

Required answer:

Thus, width of the track is 17.8 m

Knowledge booster:

• Value of π can be substituted as 22/7 or 3.14
• In exam, highlight main answer for perfection
• Solve more such questions to get good hold on it