Area of a Circle

The areas of two circles are $92 {\mathrm{cm}}^2$ and $62 {\mathrm{cm}}^2$ respectively. Find the radius (in $\mathrm{cm}$) of the circle having its area equal to the sum of the areas of the two circles.

Find the area of the blue region?

Find the area of the shaded region in the given figure.

Find the area of the shaded portion.

Sneha had a rectangular tablecloth with one side measuring 30 cm which she wanted to keep on her circular table of radius 25 cm. After keeping it on the table, she realised that the corners of the tablecloth just touched the edge of the circular table as shown in the figure.

Find the area of the table not covered by the tablecloth. 

(Note: Use $\mathrm{\pi }$ = 3.14.)

Shown below are $3$ concentric circles with centre $O$. The tangent to the second circle, $AB$, has a length of $5 \mathrm{cm}$.

Find the area of the shaded region in terms of $\pi$. Draw a rough figure and show your work.

If $SQ=QR=RS=SP=PQ, PR=21$ units, what is the area of the black portion.

Ankur, a student of class $XII,$ visited his uncle's flat with his father. He observes that the window of the house is in th form of a rectangle surmounted by a semicircular opening having perimeter $10$ mas shown in the figure. Based on the above information, answer the following question:

If $x$ and $y$ represent the length and breadth of the rectangular region, find the area $\left(A\right)$ of the window in terms of $x.$

Calculate the area of the major segment of a circle if the area of its minor segment is $54 sq. units$ and the radius is $7 units$. Use $\mathrm{\pi }=\frac{22}{7}$

Two circles of radii $r_1$ cm and $r_2$ cm $\left(r_1>r_2\right)$ touches each other internally. The sum of their areas is ${\mathrm{\pi A}}^2$ ${\mathrm{cm}}^2$ and the distance between their centres is $d$ cm, then,

If the perimeter of a circle is equal to that of a square, then find the ratio of their areas.

Let $p$ be a root of the equation $x^2-5x+7=0$ , then the area of circle with centre at $\left(p,p\right)$ and passing through point $\left(1,4\right)$ is

If the perimeter and the area of a circle are equal numerically, then the diameter of the circle is

The area swept out by a horse tied in a rectangular grass field with a rope $8\mathrm{m}$ long is 

Four circular plates of the same size having a diameter $a$ units each are placed on the square mat such that each plate touch externally the other two as shown in the figure. The area of the shaded region is;

The perimeter of a square is found to be equal to the circumference of a circle. The ratio of the area of that square to the area of that circle would be:

The area of a circle is $220 {\mathrm{cm}}^2$. If area of the square inscribed in it is $k {\mathrm{cm}}^2$, then find the value of $k$. Use $\left(\mathrm{\pi }=\frac{22}{7}\right)$

If the diameter of a circle whose area is equal to the sum of the areas of the two circles of radii $24 \mathrm{cm}$ and $7 \mathrm{cm}$ is $k \mathrm{cm}$, then find the value of $k$

$ABCD$ is a square enclosing $13$ smaller circles. If the length of the square is $\left(8+4\sqrt{3}\right) cm,$ then find the area of the shaded region.

$Q, R, S$ are the centre of three semicircles drawn as shown $A_1, A_2, A_3$ mark the area of the region in which it is written. Find the value of $\frac{3\left(A_1+A_2\right)}{A_2}.$