Question

An iron washer is made by cutting out from a circular plate of radius 10 cm, a concentric circular plate of radius 6cm. The area of the face of the washer nearly is(use $\pi =3.14$)
(a) $201c{{m}^{2}}$
(b) $206c{{m}^{2}}$
(c) $200c{{m}^{2}}$
(d) $204c{{m}^{2}}$

Answer 1

Hint: First, we have drawn a figure with the centre as A and two concentric circles with inner circle radius as r=6cm and outer circle radius as R=10cm. Then, we have to use the area(A) of the circle with radius r is given by$A=\pi {{r}^{2}}$. Then, in this question the radius of the iron washer id different as it is having one larger radius termed as (R+r) and one smaller radius as (R-r).Then, by substituting the value of R=10cm and r=6c,m in the above formula $A=3.14\left( R+r \right)\left( R-r \right)$, we get the area of the iron washer.

Complete step-by-step answer:
In this question, we are supposed to find the area of the iron washer which is cut from the circular plate of radius 10 cm with the circle of radius 6cm.
So, to visualise the figure we have the diagram as:

So, we have drawn a figure with the centre as A and two concentric circles with inner circle radius as r=6cm and outer circle radius as R=10cm.
The above mentioned inner circle radius is a concentric circular plate of radius 6cm which is to be cut out from the outer circle which is a circular plate of radius 10 cm.
Now, before calculating the area of the washer, we must be aware of the area(A) of the circle with radius r is given by:
$A=\pi {{r}^{2}}$
Now, in this question the radius of the iron washer is different as it is having one larger radius termed as (R+r) and one smaller radius as (R-r).
Then, we are also given with the condition that we should use the value of $\pi $as 3.14.
Then, now by applying the formula of the circular area of the iron washer on two different radius is given by:
$A=3.14\left( R+r \right)\left( R-r \right)$
Then, by substituting the value of R=10cm and r=6c,m in the above formula , we get:
$A=3.14\left( 10+6 \right)\left( 10-6 \right)$
Now, solve the above expression to get the final area of the iron washer as:
$\begin{align}
  & A=3.14\times 16\times 4 \\
 & \Rightarrow A=201 \\
\end{align}$
So, the area of the iron washer is $201c{{m}^{2}}$.
Hence, option (a) is correct.

Note: Here, the formula for the area of the circle is important as this question totally depends on that formula otherwise the question is very simple and straightforward. So, we must know the formula for the area(A) of the circle with radius r is given by$A=\pi {{r}^{2}}$. Also, the condition of cutting the concentric and getting the two different radius should be taken care of.