Advertisements
Advertisements
Question
A copper wire when bent in the form of a square encloses an area of 484 cm2. The same wire is not bent in the form of a circle. Find the area enclosed by the circle.
Solution
Area of the circle = 484 cm2
Area of the square = Side2
⇒ 484 = Side2
⇒ 222 = Side2
⇒ Side = 22 cm
Perimeter of the square = 4 × Side
Perimeter of the square = 4 × 22
= 88 cm
Length of the wire = 88 cm
Circumference of the circle = Length of the wire = 88 cm
Now, let the radius of the circle be r cm.
Thus, we have:
2πr = 88
`⇒ 2xx22/7xx"r"=88`
⇒ r = 14
Area of the circle = πr2
`=22/7xx14xx14`
= 616 cm2
Thus, the area enclosed by the circle is 616 cm2.
APPEARS IN
RELATED QUESTIONS
In Fig. there are shown sectors of two concentric circles of radii 7 cm and 3.5 cm. Find the area of the shaded region. Use π = `(\frac { 22 }{ 7 }).`
The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is traveling at a speed of 66 km per hour? [Use Π = 22/7]
A rectangular piece is 20m long and 15m wide from its four corners, quadrants of 3.5m radius have been cut. Find the area of remaining part.
A wire when bent in the form of an equilateral triangle encloses an area of `121sqrt(3) "cm"^2`. The same wire is bent to form a circle. Find the area enclosed by the circle.
The radius of a circular garden is 100 m. There is a road 10 m wide, running all around it. Find the area of the road and the cost of levelling it at Rs 20 per m2. [Use π = 3.14]
The radii of two concentric circles are 19 cm and 16 cm respectively. The area of the ring enclosed by these circles is
Find the area and perimeter of the circle with the following :
Diameter = 77 cm
A wire when bent in the form of a square encloses an area of 484 cm2. If the same wire is bent into the form of a circle, find the area of the circle.
The radius of the wheel of a bus is 0.7 m. How many rotations will a wheel complete while traveling a distance of 22 km?
A photograph of Billiard/Snooker table has dimensions as `1/10`th of its actual size as shown in the given figure:
The portion excluding six holes each of diameter 0.5 cm needs to be polished at rate of ₹ 200 per m2. Find the cost of polishing.
