Question

Find the number of revolution made by a circular wheel of area 1.54 m square in rolling a distance of 176 m.​

Answer 1

$\huge\underline{\bf{Given}}$

• Area of the wheel = 1.54 m²
• Distance covered by the wheel = 176 m

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$\huge\underline{\bf{To\: find}}$

• Number of revolution made by the circular wheel.

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$\huge\underline{\bf{Solution}}$

• Let r be the radius of the circular wheel.

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※ It is given that its area is 1.54 m².

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$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt{\bigstar{Area\: of\: circle = {\pi}r^2{\bigstar}}}}$

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$\tt\longmapsto{\pi r^2 = 1.54}$

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$\tt\longmapsto{\dfrac{22}{7} r^2 = 1.54}$

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$\tt\longmapsto{r^2 = 1.54 \times \dfrac{7}{22}}$

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$\tt\longmapsto{r^2 = 00.7 \times 7}$

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$\tt\longmapsto{r^2 = 0.49}$

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$\tt\longmapsto{r = \sqrt{0.49}}$

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$\tt\longmapsto{r = 0.7}$

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※ Suppose the wheel makes n revolution in rolling a distance of 176 m.

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$\boxed{\bf{\bigstar{Distance\: rolled\: in\: one\: revolution = Circumference{\bigstar}}}}$

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$\small\tt:\implies\: \: \: \: \: \: \: \: {n \times Distance\: rolled\: in\: one\: revolution = 176}$

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$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{\bf{\bigstar{Circumference = 2 \pi r{\bigstar}}}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {n \times 2 \pi r = 176}$

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$\tt:\implies\: \: \: \: \: \: \: \: {n \times 2 \times \dfrac{22}{7} \times 0.7 = 176}$

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$\tt:\implies\: \: \: \: \: \: \: \: {n = \dfrac{176 \times 7}{2 \times 22 \times 0.7}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {n = \dfrac{\cancel{176} \times 7}{\cancel{44} \times 0.7}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {n = \dfrac{16 \times 7}{4 \times 0.7}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {n = \dfrac{112}{2.8}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {\boxed{n = 40}}$

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Hence, the circular wheel makes 40 revolutions.

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Answer 2

Given :-

• Area of circular wheel = 1.54 m²
• distance = 176 m

To find :-

• what is the number of revolution wheel ?

Solution :-

• Let radius of the circle = r m

➤ Area of the circle ( A ) = πr² ---( 1 )

➤ Area = 1.54 m²---( 2 )

so, equation :-

( 1 ) = ( 2 )

➤ πr² = 1.54 m²

⇒ ( 22 / 7 ) r² = 1.54

⇒ r² = 1.54 × 22/7

⇒ r² = 0.07 × 7

⇒ r² = 0.49

⇒ r = √0.49

⇒ r = 0.7

• Let the number of revolutions = n
• One revolution = perimeter of the circle (P)

⇒ n × 2πr = 176

⇒ n × 2 × 22/7 × 0.7 = 176

⇒ n = 176 × 7 / 2 × 22 × 0.7

⇒ n = 16 × 7 / 4 × 0.7

⇒ n = 112 / 2.8

⇒ n = 40

➤ Number of revolutions ( n ) = 40

Hence, the number of revolution wheel is 40.

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