Q. 24.1( 8 Votes )
A wire was bent into a circle of diameter 4 centimetres. What would be the diameter of a circle made by bending a wire of half the length?
Answer :
Diameter of circle = 4 cm
Length of wire = Circumference of circle
If r = radius of circle
Circumference of circle = 2 × π × r=2 × π × 4
=8 × π
If length of wire is halved,
Circumference is also halved
∴ New Circumference = 1/2 × (8 × π)= 4 × π
Let r’be new radius
∴ 2 × π × r'= New Circumference = 4 × π
∴ r’ = 
Hence, New diameter = 2 × r'= 2 × 2=4 cm
Rate this question :
Master Theorems in Circles42 mins
R.D. Sharma | Circle40 mins
Genius Quiz | Rolling Around Circles49 mins
Bonus Questions on Measures of Central Tendency43 mins
Quiz | Solve Imp. Qs. on Circle44 mins
Quiz | Lets Roll on a Circle45 mins
Let's Solve Good Questions on Circle41 mins
In this picture, the circles have the same centre and the line drawn is a diameter of the large circle. How much more is the perimeter of the large circle than the perimeter of the small circle?
Draw a square and a circle through all four vertices. Draw diameters parallel to the sides of the square and draw a polygon joining the end points of these diameters and the vertices of the square.
Prove that this polygon is a regular octagon.
Kerala Board Mathematics Part-1The perimeter of a circle of diameter 2 metres was measured and found to be about 6.28 metres. How do we compute the perimeter of a circle of diameter 3 metres, without measuring?
Kerala Board Mathematics Part-2A wire was bent into a circle of diameter 4 centimetres. What would be the diameter of a circle made by bending a wire of half the length?
Kerala Board Mathematics Part-2In the picture below, a regular hexagon, square and a rectangle are drawn with their vertices on a circle. Calculate the perimeter of each circle.
In all the pictures, below, centres of the circles are on the same line. In the first two pictures, the small circles are of the same diameter.
Prove that in all pictures, the perimeters of the large circle is the sum of the perimeters of the small circles.
Kerala Board Mathematics Part-2An isosceles triangle with its vertices on a circle is shown in this picture.
What is the perimeter of the circle?
Kerala Board Mathematics Part-2Calculate the perimeter of a square with vertices on a circle of diameter 1 centimetre.
Kerala Board Mathematics Part-2