Advertisements
Advertisements
Question
A wire in the form of a circle of radius 42cm. It is bent into a square. Determine the side of the square and compare the area of the regions enclosed in the two cases.
Advertisements
Solution
Let the side of the square = s and the radius of the circle = r
The Circumference of a circle with radius r = 2πr
The Circumference of a Circle with radius 42
= 2π x 42
= 264cm
The Area of a Circle with radius r
= πr2
= π(42)2
= 5544cm2
The Circumference of the Circle
= Perimeter of the square
⇒ Perimeter of the Square = 264cm
⇒ 4s = 264cm
⇒ s = 66cm
Area of a Square with side s = 4s2
Area of a Square with side 66
= 4(66)2
= 4356cm2
Ratio of Area of the Circle to the Area of the Square
= 5544:4356
= 14:11.
APPEARS IN
RELATED QUESTIONS
In circle of radius 6cm, chord of length 10 cm makes an angle of 110° at the centre of circle find Area of the circle
A playground has the shape of rectangle, with two semicircles on its smaller sides as diameters, added to its outside. If the sides of rectangle are 36m and 24.5m. find the area of playground.
The circumference of a circle is equal to the perimeter of a square. The area of the square is 484 sq. m. Find the area of the circle.
A cylindrical bucket, whose base radius is 20 cm, is filled with water to a height of 25 cm. A heavy iron spherical ball of radius 10 cm is dropped to submerge completely in water in the bucket. Find the increase in the level of water.
The radius of a circular garden is 56 m. What would it cost to put a 4-round fence around this garden at a rate of 40 rupees per metre?
The diameter of a wheel is 1.4m. How many revolutions does make in moving a distance of 2.2km?
The radius of a circular plot is 7.7 metres. How much will it cost to fence the plot with 3 rounds of wire at the rate of 50 rupees per metre?
A wheel of a car covers a distance of 3520 cm in 20 rotations. Find the radius of the wheel?
The numerical value of the area of a circle is greater than the numerical value of its circumference. Is this statement true? Why?
The moon is about 384000 km from earth and its path around the earth is nearly circular. Find the length of path described by moon in one complete revolution. (Take π = 3.14)
