Question

A wheel takes 500 revolutions to cover 11 kilometre find its radius​

Answer 1

Given :

• A wheel takes 5000 revolutions to cover 11 km.

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To Find :

• It's radius = ?

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★ Procedure :

So, as per the question we are provided that, on covering 11 km, a wheel takes 5000 revolutions. And we are asked to find its radius.

For solving this question, firstly we need to calculate the distance covered in one revolution. After this, we will calculate the radius [as per asked in the question].

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Calculation :

☯ Let the radius of the wheel be r cm.

We know that,

• Distance covered in 1 round by a circle = $\bf 2 \pi \: r$ or $\bf peri$

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Distance covered in one revolution = $\bf \: 2 \pi \: r$

Distance covered in 500 revolutions = $\bf \: 11 \: km$

$\bf \longrightarrow \: 5000 \: \times 2\pi \: r \: = \: 11 \: km \\ \\ \bf \longrightarrow \: 5000 \: \times \: 2 \: \times \dfrac{22}{7} \: \times r \: = 11 \: km \\ \\ \bf \: \longrightarrow \: r = \dfrac{ \cancel 11 \times 7}{5000 \times \cancel 44} \\ \\ \bf \longrightarrow \dfrac{7}{20000} \: km$

We know that,

• 1 km = 1000 m

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$\bf \longrightarrow \: \dfrac{7 \: \times \: 1000}{20000} \\ \\ \bf \longrightarrow \: \dfrac{7}{ \cancel{20}} \: \times \: { \cancel{100}}^{5} \\ \\ \bf \longrightarrow \: 7 \: \times \: 5 \\ \\ \bf \longrightarrow \: 35 \: cm$

$\therefore$ The radius of the wheel is 35 cm.

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★ More to know :-

» $\sf \: Area \: of \: circle \: = \pi \: r^2$

» $\sf \: Circumference \: of \: a \: circle \: = \: 2 \pi \: r$

• $\sf \: d \: = 2 \: r$

• $\sf \: r = \dfrac{d}{2}$

» $\sf \: Value \: of \: \pi = \dfrac{22}{7} \: or \: 3.14$

» $\sf \: Value \: of \: r = radius$