Question

The area of the circular ring included between two concentric circles of radii 14 centimeter and 10.5 centimeter to the closest integer is

Answer 1

HINT: Let the two circles be ‘A’ and ‘B’. ‘A’ is the circle with radius 14 cm and the radius of ‘B’ is 10.5 cm. To solve this question and to find the area of the ring, we will have to subtract the area of the circle ‘B’ from the area of the circle ‘A’.

Complete step-by-step solution -
To find the area of the circles, we will have to use the following formula:-
AREA OF CIRCLE: \[\pi {{r}^{2}}\]
Where, the value of \[\pi =\dfrac{22}{7}\] and ‘r’ stands for the radius of the circle whose area is to be calculated.
And hence, we will be able to find the area of the ring.

Let us now solve the question.
Firstly, we will calculate the area of the circle A.
As mentioned in the hint provided above, the formula that we use to find or calculate the area of a circle is \[\pi {{r}^{2}}\] and the value of \[\pi =\dfrac{22}{7}\] and ‘r’ stands for the radius of the circle whose area is to be calculated.
We know that the radius of circle A is 14 centimeter.
So, area of the circle A = \[\pi {{r}^{2}}\]
                                         = \[\dfrac{22}{7}\times ~{{\left( 14 \right)}^{2}}\]
                                         = \[\dfrac{22}{7}\times ~196\]
                                         = \[22\times ~28\]
                                         = 616 square cm
So, the area of the circle ‘A’, i.e. the outer circle is 616 square cm.
Let us now calculate the area of the circle ‘B’, i.e. the inner circle.
So, area of the circle B = \[\pi {{r}^{2}}\]
                                         = \[\dfrac{22}{7}\times ~{{\left( 10.5 \right)}^{2}}\]
                                         = \[\dfrac{22}{7}\times ~110.25\]
                                         = \[22\times ~15.75\]
                                         = 346.5 square cm
So, let us now subtract the area of the inner circle from the area of the outer circle, i.e. the area of the circle ‘B’ from that of the circle ‘A’.
(616 – 346.5) square cm = 270.5 square cm.
So, the area of the ring is 270.5 square cm and on rounding it off to the nearest integer, we get the area of the ring as 271 square cm.

NOTE:- One must do all the calculations in this question very carefully. If the student makes any mistake in the calculations, then the answer so obtained will not be correct.
Also not only in this question, the students must be very careful while solving any such questions as if there is any mistake in the calculus, then the answer can come out to be wrong.