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The area of a circle is 38.5 sq. cm. Its circumference is
Given: Area of the circle = πr^{2}  38 5 sq. cm
∴ Circumference of the circle
The area of the square that can be inscribed in a circle of radius 12 cm is
According to question, Diameter (BD) = 2 x radius = 2 x 12 = 24 cm
∴ Area of square
If the area of a circle is equal to the area of a square, then the ratio of their perimeters is
Let the radius of the circle be rr and the side of the square be a.a. Then according to the question,
Now, Ratio of their perimeters
A piece of wire 20cm long is bent into the form of an arc of a circle subtending an angle of 60 at its centre. The radius of the circle is
The area of a sector of a circle with radius 21cm and sector angle 120^{∘} is
Area of the sector
⇒ Area of the sector
= 462 sq. cm
The circumference of a circle whose diameter is 4.2cm is
Given : Diameter (d) = 4.2 cm
∴ Circumference
The area of the circle that can be inscribed in a square of side 10cm is
Since if a circle inscribed a square. then the radius of the circle is half of to side of square.
∴ Radius = 10/2 = 5 cm
∴ Area of the circle = πr^{2} = π(5)^{2} = 25π sq. cm
The area of a square that can be inscribed in a circle of radius 10cm is
Given: Radius (r) = 10 cm
Let side of the square be x cm
Now. using Pythagoras theorem.
x^{2 }+ x^{2} = (2r)^{2 }⇒ 2x^{2} = (20)^{2}
⇒ 2x^{2} = 400 ⇒ x^{2} = 200 sq. cm
Therefore. area of the square = 200 sq. cm.
A square of side 7cmis inscribed in a circle. The area enclosed between the circle and the square is
The angle described b the minute hand between 4.00 pm and 4.25 pm is
Time duration between 4.00 om and 4.25 pm = 25 minutes
∵ Angle described by minute hand in 60 minutes = 360°
∴ Angle described by minute hand in 25 minutes
The length of the wire is 66m. The number of circles of circumference 13.2cm can be made from the wire is
Given: Length of wire = 66 m = 6600 cm and Circumference = 13.2 cm
If the perimeter of a circle is equal to that of a square, then the ratio of their areas is
Let the radius of the circle be rr and side of the square be a. Then, according to question,
Now, ratio of their areas,
If the area and circumference of a circle are numerically equal, then its radius is
Let radius of the circle berunits.
∴ Area of the circle = Circumference of the circle
On a square handkerchief, nine circular designs each of radius 7cmare made. The area of the remaining portion of the handkerchief is
Here Side of square ABCD = AB = 3 x diameter of circular design
⇒ AB = 3 x (2 x 7) = 42 cm
∴ Area of square = 42 x 42 = 1764 cm^{2}
And Area of one circular design
And Area of one circular design
∴ Area of 9 circular designs = 154 x 9 = 1386 sq. cm
∴ Area of remaining portion of handkerchief = 1764  1386 = 378 sq. cm
A horse is tied to a peg at one corner of a square shaped gross field of side 25m by means of a 14m long rope. The area of that part of the field in which the horse can graze is
Area of the shaded region
Area of the shaded region
Area of the shaded region = 154 sq. cm
Let radius of the protractor be r
∴ Perimeter of protractor = Perimeter of semicircle + Diameter of semicircle ⇒ Perimeter of protractor = πr+2r
The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36cm and 20cm is
Let required radius be R. Then according to the question,
If the radius of a circle is increased by 100%, then its area is increased by
Area of the circle with radius r =πr^{2}
Now, New Radius = r + 100% of r = r + r = 2r
∴ New Area = π(2r)^{2}  4πr^{2}
∴ Increased Area = 4πr^{2}  πr^{2} = 3πr^{2}
And Area increased in
If the area of a circle is ‘A’, radius of the circle is ‘r’ and its circumference is ‘C’, then
Here, Area of circle (A) = πr^{2} and Circumference of circle (C) = 2πr
Putting value of C in A = πr^{2}, we get
A light house throws light forming sector of radius 21 m with central angle 120^{∘}. The area covered by it is
Area of the sector
⇒ Area of the sector
⇒ Area of the shaded region = 462 sq. cm
The circumference of a circle exceeds its diameter by 120cm, then its radius is
If the circumference of a circle and the perimeter of a square are equal, then
Let the radius of the circle be r and side of the square be a.
Then, according to question,
2πr = 4a
Now, ratio of their areas,
Therefore, Area of the circle > Area of the square
The distance around the circle is called its circumference
The area of a quadrant of a circle whose circumference is 88cm is
If a chord of a circle of radius14cm subtends a right angle at the centre of the circle, then the area of the sector is
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