Finding the Greatest Inscribed Circle Area
The question asks for the area of the greatest circle that can fit inside a square with a side length of 21 cm.
Relating Square Side to Circle Diameter
The largest possible circle that can be inscribed within a square will have a diameter equal to the side length of the square.
- Square side length, $s = 21$ cm.
- Diameter of the greatest inscribed circle, $d = s = 21$ cm.
Calculating the Circle's Radius
The radius ($r$) is half the diameter ($d$).
Calculation: $r = \frac{d}{2} = \frac{21 \text{ cm}}{2} = 10.5$ cm.
Computing the Circle's Area
The formula for the area ($A$) of a circle is $A = \pi r^2$. We use the approximation $\pi \approx \frac{22}{7}$.
Calculation: $A = \pi r^2$ $A = \frac{22}{7} \times (10.5 \text{ cm})^2$ $A = \frac{22}{7} \times (\frac{21}{2} \text{ cm})^2$ $A = \frac{22}{7} \times \frac{441}{4} \text{ cm}^2$ $A = \frac{11 \times 441}{7 \times 2} \text{ cm}^2$ $A = \frac{11 \times 63}{2} \text{ cm}^2$ $A = \frac{693}{2} \text{ cm}^2$ $A = 346.5 \text{ cm}^2$
Therefore, the area of the greatest circle that can be inscribed inside the square is 346.5 cm$^2$.
Similar Questions
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Important Questions from Plane Figures
If length of a rectangle is increased to its three times and breadth is decreased to its half, then the ratio of the area of given rectangle to the area of new rectangle is:
The width of the path around a square field is 4.5 m and its area is 105.75 m 2. Find the cost of fencing the field at the rate of Rs. 100 per meter.
What is the area of the square (in cm 2) whose vertices lie on a circle of radius 5 cm?
The circumcentre of an equilateral triangle is at a distance of 3.2 cm from the base of the triangle. What is the length (in cm) of each of its altitudes?
The perimeter of a circular lawn is 1232 m. There is 7 m wide path around the lawn. The area (in m 2) of the path is:
Take \(\left(\pi=\frac{22}{7}\right)\)
