NCERT Solutions for Class 4th Maths Chapter 11 . Holes and Cuts — Holes and Cuts
Book page 1663 Updated on2026-09-19
Q1.
Mini has made this design by folding and cutting paper. Now it’s your turn! Take a square sheet of paper. Do as instructed below.The square sheet folded over and over, and then snipped along the folded edges.Mini’s design, opened out.
Answer
Mini folded a square sheet again and again and then cut small bits off the folded edges.
Mini’s design after the folded paper is opened out.
Take a square sheet. Fold it in half — you get a rectangle.
Fold it in half again — you get a smaller square.
Fold it once more along the corner — you get a triangle.
Snip small bits off the edges of the folded triangle.
Open it out slowly.
Why it happens: Each fold doubles the layers. One snip cuts through every layer at once, so the same little hole appears many times, in a neat pattern.
Q2.
Challenge 1: Where would the hole and cut appear when you open the paper?
Answer
Rani folded twice, so her paper has 4 layers. Every cut she makes is repeated 4 times when the paper opens.
Rani’s folded paper after cutting. The top edge and the left edge are folds.
When she opens it out:
The corner cut was at the corner where the two open edges meet, so all four corners of the square get cut off.
The square cut on the folded (left) edge opens into 2 full holes inside the paper, one above the middle and one below it.
The square cut on the open (right) edge stays on the border. It shows up as 4 notches — two on the left side and two on the right side.
The opened sheet: four corners cut, four notches on the sides, two holes inside.
Why it happens: A cut on a folded edge loses its fold when you open it, so the two halves of the cut join into one whole hole. A cut on an open edge stays a notch on the border.
Q3.
Challenge 2: Fold a piece of paper once; put two cuts in the middle as shown. How many sides will this shape have when you open the folded paper?The paper folded once, with two cuts made in the middle of the folded edge.
Answer
The two cuts are made on the folded edge, in the middle.
The paper folded once, with two cuts made in the middle of the fold.
Cuts made on the folded paper = 2 Each cut becomes 2 sides when the fold opens 2 × 2 = 4 sides
So the shape that opens out has 4 sides. It is a four-sided hole, shaped like a diamond.
The opened paper with the four-sided hole; its sides are numbered 1 to 4.
Why it happens: The fold acts like a mirror. Whatever you cut on one side of the fold is copied on the other side when the paper opens.
Q4.
Challenge 3: Fold a paper twice. Where would you cut to make a square hole in the center of the paper? How many cuts are required?
Answer
Cut at the corner where the two folded edges meet. You need only 2 cuts.
The paper after two folds. The circled corner is where both folds meet.
Snip a small square off that corner, using two straight cuts:
Left: the two cuts at the folded corner. Right: the square hole in the middle of the opened sheet.
Sides of the small square = 4 2 sides are already the folded edges Cuts needed = 4 − 2 = 2
Why it happens: The corner where both folds meet is the centre of the whole sheet. The two folded edges become two sides of the hole by themselves, so only the other two sides have to be cut.