Question

The length and breadth of a rectangular sheet is given as 35 cm and 22 cm. Find out the area of the largest circle that can be cut out.

Answer 1

Hint: The largest circle means the largest diameter possible means the short side of the rectangle because extending diameter more than that means that the circle formed will not be complete.

Area of circle = $\pi {{r}^{2}}$.

Complete step-by-step answer:


To find out the largest area we have to find the largest diameter.

The largest Diameter is clearly along the shortest side as any Larger and we won’t be able to make a complete circle.

So, the diameter is equal to 22cm

Now we have to find the area of the circle.

Formula for area of circle = $\pi {{r}^{2}}$where r is equal to radius of the circle
Radius of the circle = 11 cm.

Now substituting the values in the formula for the area of the circle we get the following equation.

Area of circle = $\pi {{11}^{2}}$

Now pi is an irrational number but for mathematical purposes we take π = 3.14 or π = $\dfrac{22}{7}$

In this case we will take π = 3.14

So, area of circle = 3.14(11)2

= 379.94 cm2

Largest area of the circle that can be cut from the rectangle is equal to 379.94 cm2

Note: For a proper circle we need the shorter side otherwise we won’t have a perfect circle. Also, the side gives the diameter, don’t forget to convert it into radius before converting or else we will get a wrong answer.