Question

diameter of A wheel of a car is 70 cm find the distance covered by the car during the time in which the wheel makes 1000 revolutions.​

Answer 1

❆ Concept :-

Whenever we are provided with Diameter of a wheel or radius of a wheel and the number of revolutions, and are asked to find out the distance covered. We will always use the formula :-

$\boxed{ \orange \bigstar \: \sf \green {distance \: covered \: = circumference \: \times number \: of \: revolutions}}$

When a wheel revolves it covers a certain distance which is equal to the circumference of the wheel. Therefore, the total distance covered can be derived by multiplying the number of revolutions with the circumference of the wheel. Using this concept, the given formula has been derived.

$\orange \bigstar \: \sf\red {Given :-}$

• Diameter of a wheel = 70 cm, so r = 70/2 = 35 cm
• Number of revolutions = 1000

$\orange \bigstar \: \sf \blue {To \: Find :-}$

• The distance covered by the car.

$\orange\bigstar \: \sf \pink{Solution :-}$

We know that,

$\boxed{ \orange \bigstar\sf \: \green { circumference = 2 \pi r}}$

$\sf \leadsto \: circumference \: = 2 \times \frac{22}{7} \times 35cm$

❆ Until and unless we aren't asked to take the value of pi as 3.14, we will take the value as 22/7. As it makes the calculation easier by using the cancellation method. As we can see, here, 7 will cancel out 35 by 5. Hence, it is making the calculation easier.

$\sf \leadsto \: circumference \: = 2 \times \frac{22} { \cancel7} \times \cancel{35 } \: \: \: \: ^{5} \: \: \: \: \: \\ \sf \leadsto \: circumference \: = 2 \times22 \times 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \leadsto \: circumference \: = 10 \times 22 = 220 \: cm$

Now, we have found out the circumference. Therefore, to find out the distance we can simply put the given and derived value in the formula of distance covered.

$\sf \leadsto \: distance \: covered \: = 220 \times 1000 \\ \sf \leadsto \: distance \: covered \: = 220000 \: cm \:$

$\sf \leadsto \: distance \: covered \: ( \: in \: m \: ) = \frac{2200 \cancel{00}}{1 \cancel{00}} = 2200 \: m \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \leadsto \: distance \: covered \: ( \: in \: km \: ) = \frac{22 \cancel{0000}}{10 \cancel{0000}} = \frac{22}{10} = 2.2 \: km$

Answer 2

Step-by-step explanation:

$\tt{\implies}circumference=2×722×355 \\ \tt{\implies}⇝circumference=2×22×5 \\ \tt{\implies}⇝circumference=10×22=220cm</p><p> \\ </p><p>\tt{\implies}Now, we have found out the circumference. \\ \tt{\implies}Therefore, \\ to \: find \: out \: the \: distance \: we \: can \: simply put \: the \: given \: and \: derived \: value \: in \: the \: formula \: of \: distance \: covered. \\ </p><p></p><p>\tt{\implies}\begin{gathered}\sf \leadsto \: distance \: covered \: = 220 \times 1000 \\ \sf \leadsto \: distance \: covered \: = 220000 \: cm \: \end{gathered} \\ \tt{\implies}⇝distancecovered=220×1000 \\ \tt{\implies}⇝distancecovered=220000cm \\ </p><p></p><p>\begin{gathered}\sf \leadsto \: distance \: covered \: ( \: in \: m \: ) = \frac{2200 \cancel{00}}{1 \cancel{00}} = 2200 \: m \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \leadsto \: distance \: covered \: ( \: in \: km \: ) = \frac{22 \cancel{0000}}{10 \cancel{0000}} = \frac{22}{10} = 2.2 \: km\end{gathered} \\ \tt{\implies}⇝distancecovered(inm)=100220000 =2200m \\ \tt{\implies}⇝distancecovered(inkm)=100000220000=1022=2.2km \\ </p><p></p><p>$