Question

A circular disc of area $\left( 0.49\pi \right){{m}^{2}}$ rolls down a length of $1.76km$. How many revolutions does it make?
$\left( A \right)\text{ 300}$
$\left( B \right)\text{ 400}$
$\left( C \right)\text{ 500}$
$\left( D \right)\text{ 600}$

Answer 1

Hint: In this question we have been given with a circular disc which has an area of which rolls down a length of $1.76km$. We will first use the area of a circle formula which is $\pi {{r}^{2}}$and find the radius of the circle which is given as $r$. We will then find the circumference of the circle using the formula $2\pi r$. We will then divide the total length travelled by the circle with the circumference of the circumference to get the number of revolutions made by the circular disc.

Complete step by step solution:
We know that the area of the circular disc is $\left( 0.49\pi \right){{m}^{2}}$. We know that the formula to find the area of a circle is given as:
$\Rightarrow \pi {{r}^{2}}$
On equating the area of the circular disc with the formula, we get:
$\Rightarrow \pi {{r}^{2}}=0.49\pi $
On cancelling $\pi $ from both the sides, we get:
$\Rightarrow {{r}^{2}}=0.49$
On taking square root on both the sides, we get:
$\Rightarrow r=\sqrt{0.49}$
Now we know that $0.49=0.7\times 0.7$ therefore, on substituting, we get:
$\Rightarrow r=\sqrt{0.7\times 0.7}$
On taking the root, we get:
$\Rightarrow r=0.7$, which is the radius of the circle.
Now the circumference of a circle is given with the formula as:
$\Rightarrow \text{circumference}=2\pi r$
On substituting the value of $r=0.7$, we get:
$\Rightarrow \text{circumference}=2\pi \times 0.7$
On substituting the value of $\pi =\dfrac{22}{7}$
$\Rightarrow \text{circumference = }2\times \dfrac{22}{7}\times 0.7$
On simplifying, we get:
$\Rightarrow \text{circumference = }44\times 0.1$
On multiplying the terms, we get:
$\Rightarrow \text{circumference = }4.4m$, which is the required circumference.
Now the total length covered by the disc is $1.76km$.
Now since $1km=1000m$, we can write $1.76km$ as $1760m$.
The number of revolutions made by the disc would be the total distance covered divided by the circumference of the circle, which can be written as:
$\Rightarrow \text{Number of revolutions = }\dfrac{1760}{4.4}$
On simplifying, we get:
$\Rightarrow \text{Number of revolutions = 400}$ therefore, the correct option is $\left( \text{B} \right)$.

So, the correct answer is “Option B”.

Note: It is to be remembered that when dealing with measurement sums the units of the quantities should always be the same. In this question we have used meters as the unit for simplification which is why we converted the distance of $1.76km$ to meters as direct division of kilometers and meters is invalid.