Advertisements
Advertisements
प्रश्न
If a square in inscribed in a circle, find the ratio of the areas of the circle and the square.
Advertisements
उत्तर
If AB = x, AC = x√2
Diameter of the circle = diagonal of the square
⇒ 2r = x√2
⇒ r = `(xsqrt2)/2`
Area of the circle = πr2
= π`((x sqrt2)/2)^2`
= π`(( x^2 2)/4)`
= `(πx^2)/2`
Area of the square = x2
Required ratio = `((πx^2)/2 )/x^2`
= `π/2`
= `22/7 xx 1/2`
= `11/7`
Hence, the required ratio is 11 : 7.
APPEARS IN
संबंधित प्रश्न
Find the perimeter of the adjoining figure, which is a semicircle including its diameter.
The area of rectangle is `192cm^2` and its perimeter is 56 cm. Find the dimensions of the rectangle.
The cost of painting the four walls of a room 12 m long at `₹ 30 per m^2 is ₹ 7560 per m^2` and the cost of covering the floor with the mat at ₹` 25 per m^2 is ₹ 2700 `. find the dimensions of the room.
In the given figure ABCD is quadrilateral in which diagonal BD = 24 cm, AL ⊥ BD and CM ⊥ BD such that AL = 9cm and CM = 12 cm. Calculate the area of the quadrilateral.
In the following figure, an equilateral triangle ABC of side 6 cm has been inscribed in a circle. Find the area of the shaded region. (Take π = 3.14).
The perimeter of a triangle is 30 cm and the circumference of its incircle is 88 cm. The area of the triangle is
If the area of a square is same as the area of a circle, then the ratio of their perimeters, in terms of π, is
A square is inscribed in a circle. Find the ratio of the areas of the circle and the square.
The length of an arc of the sector of angle θ° of a circle with radius R is
A lawn is in the shape of a semicircle of diameter 42m. the lawn is surrounded by a flower bed of width 7m all round. Find the area of the flower bed in m2.
