Question

From a circular card sheet of radius 14 cm, a square of 4 cm is removed as shown in the figure below. Find the area of the remaining sheet. \[\left( {\pi = \dfrac{{22}}{7}} \right)\]

Answer 1

Hint: We have to only find the area of the circle of given radius and square of the given side and then we will subtract the area of the square from the area of the circle which will be the required area asked to find.

Complete step-by-step answer:
Now as we know that if any part of any shape is cut out or removed then the area of the remaining shape will be equal to the area of removed part subtracted from the area of the original shape.
And here we are given a shape circle and then the square is removed from it.
So, the area of the remaining shape will be equal to the area of the circle – area of square.
Now as we know that the formula for the area of a circle is \[\pi {r^2}\], where r is the radius of the circle.
Here the radius of the circle given is 14 cm.
So, the area of the circle will be \[\pi {\left( {14} \right)^2} - 196\pi = 196 \times \dfrac{{22}}{7} = 28 \times 22 = 616{\text{ }}c{m^2}\]
And the formula for the area of the square is \[{a^2}\], where a is the side length of the square.
Here the side length of the square removed is 4 cm.
So, the area of the removed square will be \[{\left( 4 \right)^2} = 16{\text{ }}c{m^2}\]
Now, the area of the remaining sheet will be = area of the circle – area of the square = 616 – 16 = 600 \[c{m^2}\].
Hence, the area of the remaining sheet will be 600 \[c{m^2}\].

Note: Whenever we come up with this type of problem where we are given the shape of the original sheet (here circle) and then some part of that sheet is removed from it (here square) and asked to find the area of the remaining sheet then we first, find the area of the original sheet (here circle) using formula for area of that shape i.e. \[\pi {r^2}\], and the area of the removed part of the sheet (here square) by using formula of area i.e. \[{a^2}\] . And then subtract the area of the removed part from the area of the original sheet to get the area of the remaining sheet. And this will be the easiest and efficient way to find the solution of the problem.