NCERT Solutions for Class 4th Maths Chapter 1 Folding a circle of paper to find its diameters — Amazing Circles
Book page 17 Updated on2026-09-19
Q1.
The length of all the creases are ___________. (Equal/Unequal)
The circular paper after it has been folded in half three different ways.
Answer
The lengths of all the creases are Equal.
Fold the round paper in half and press the fold. Open it and measure the crease
with a thread.
Fold it in half a different way. Open it and measure that crease too.
Fold it in half once more, again in a different way, and measure.
Every time the thread comes out the same length.
Why it happens: Each fold cuts the circle into two matching
halves, so the crease has to pass right through the middle. A line through the middle of
a circle is always the longest line across it — and it is the same length whichever
way you turn it.
Q2.
These creases are called diameters of the circle. Discuss where the centre is. Do you notice that all the diameters pass through the centre?
The circular paper after it has been folded in half three different ways.
Answer
The centre is the point where all the creases cross.
Open the paper and look at the three creases together.
They do not cross at three different places — they all cross at
one single point.
That point is the centre of the circle. Yes, every diameter passes through
it.
The same creases. They all cross at one point.
Why it happens: A fold in half puts one half of the circle
exactly on the other half, and that can happen only if the fold goes through the centre.
So every diameter must pass through the centre — and therefore all of them meet
there.
Check it yourself: Measure from the crossing point to the border
in any direction. The distance is the same every time.
Q3.
Measure the length of the creases from the center to the border of the circle. This is called the radius of the circle.
A circle with one diameter and one radius drawn.
Answer
From the centre to the border is the radius, and it is
half of the diameter.
Take a thread and measure from the centre to the border along one crease.
Do it again along another crease, and again along a third.
All these lengths come out equal.
Sample measurement
Diameter (the whole crease) = 8 cm
Centre to border = 8 ÷ 2 = 4 cm
So the radius = 4 cm
Why it happens: The centre cuts every diameter into two equal
parts, because the centre is the middle of the circle. Each of those parts is a
radius.
Q4.
Discuss if there is any relationship between the radius and the diameter of a circle.
A circle with one diameter and one radius drawn.
Answer
Yes. The diameter is always double the
radius, and the radius is always half the diameter.
diameter = radius + radius
So diameter = 2 × radius
and radius = diameter ÷ 2
Some examples
Radius
Diameter
3 cm
3 + 3 = 6 cm
5 cm
5 + 5 = 10 cm
7 cm
7 + 7 = 14 cm
10 cm
10 + 10 = 20 cm
Why it happens: A diameter runs from the border, through
the centre, to the border again. That is one radius up to the centre and one more radius
onwards — two radii in all.