Advertisements
Advertisements
Question
A wire, when bent in the form of a square; encloses an area of 196 cm2. If the same wire is bent to form a circle; find the area of the circle.
Advertisements
Solution
Area of Square = 196 cm2
Side of Square = `sqrt("Area")` = `sqrt(196)` = 14 cm
Perimeter of Square = 4 x 14 cm
i.e. length of wire = 56 cm
Circumference of circle = 56 cm
2πr = 56
`2 xx 22/7 xx r = 56`
`r = (56 xx 7)/(2 xx 22)`
`r = 98/11` cm
`therefore "Area of circle enclosed" = pir^2`
= `22/7 xx 98/11 xx 98/11`
= `2744/11`
= 249.45 cm2
APPEARS IN
RELATED QUESTIONS
A footpath of uniform width runs all around the inside of a rectangular field 54 m long and 35 m wide. If the area of the path is 420 m2, find the width of the path.
A square of diagonal 8 cm is inscribed in a circle. Find the area of the region lying outside the circle and inside the square.
A rectangular park is 100 m by 50 m. It is surrounding by semi-circular flower beds all round. Find the cost of levelling the semi-circular flower beds at 60 paise per square metre (use π = 3.14).
In the following figure, ABC is a right-angled triangle, ∠B = 90°, AB = 28 cm and BC = 21 cm. With AC as diameter a semicircle is drawn and with BC as radius a quarter circle is drawn. Find the area of the shaded region correct to two decimal places.
In the given figure, ∆ABC is right-angled at A. Semicircles are drawn on AB, AC and BC as diameters. It is given that AB = 3 cm and AC = 4 cm. Find the area of the shaded region.
The area of a sector of angle θ° of a circle with radius R is ______.
The diameters of three wheels are in the ratio 2 : 4 : 8. If the sum of the circumferences of these circles be 132 cm, find the difference between the areas of the largest and the smallest of these wheels.
In a grassland, a sheep is tethered by a rope of length 4.9 m. Find the maximum area that the sheep can graze
The area of a circle is 154 cm2. Its diameter is ____________.
A pendulum swings through an angle of 30∘ and describes an arc 8.8 cm in length. Find the length of the pendulum in cm.
