folding and unfolding

 A paper sheet in the shape of square is folding as shown in the sketch. After folding two protruding corners are cut and remove as shown in the sketch(shaded portion). after cutting that portion unfold the paper. what shape you will get? choose the correct shape.

don't use a paper for solving this problem. first you try to visualize the folding and unfolding, then try to find out the answer, if you want to boost your creativity.  if you cannot find out the true shape, nothing to worry. use a paper to find out the true shape.

problems of area

in the sketch some area is shaded. now what would be the ratio

refrigerator and ice cubes

a special refrigerator compartment having a size of 0.8m in length, 0.4m width and 0.5m height. this compartment is having a top mounted door. how many ice cubes we can store in this refrigerator  if each cube is 0.2m on an edge?

the case of symmetry

A figure that can be folded over along a straight line so that the result is two equal halves which are then lying on top of one another with no overlap is said to be have a line of symmetry.
Now question is,
which of the following shapes have only one line of symmetry

1. circle 
2. square
3. rectangle
4. equilateral triangle
5. isosceles triangle

the ratio

a square is shown in the sketch. some area of the square is shaded and rest of the area is unshaded. one side of the square is 5 units. what would be the ratio of Area of shaded portion to the area of unshaded portion.

make a perfect square

a long rectangular paper strip which is equally divided into 5 squares as shown in the sketch is given. you can fold it and cut. can you make a perfect square using the paper pieces. you are allowed to make exactly two cuts only.



solution:
fold the paper strip through the center. then cut the strip as shown in the sketch using red lines. you will get 4 pieces. by arranging those paper pieces as shown in the last sketch, you can make the perfect square.

cut a square from rectangle

A paper in rectangular shape is provided. objective is to cut a square shape with maximum area.

crossword of geometrical shapes

   Down

1. Volume of a cone
2. Volume of a sphere
3. Surface area of cube
4. Volume of a square prism
5. Volume of hemisphere
6. Curved surface area of cone
7. Area of a circle

Right

     8.       Curved surface area of a cylinder

     1.       Volume of a pyramid

     9.       Curved surface area of hemisphere

   10.       Surface area of sphere

         Left

              11.       Total surface area of hemisphere

              12.       Volume of a cube

The packaging design

Two views of a box is shown in the sketch. the packaging of the box having a black and white pattern on its surface.

Choose the correct packaging design by which, the box is covered from the options A,B,C and D.

The shape shown in the sketch below, obviously,  is that of a square attached to half of another similar square, divided diagonally:

Can you divide it into four pieces all of precisely the same shape and size?

                                               Courtesy: Shakunthala Devi's Puzzles to puzzle you

Orthographic views of an object is shown below. The front view, top view and side view are same. Draw the isometric view of this object.

Three balls of same size, initially at rest are rolling down from an inclined plane as shown in fig. Balls are coming to rest at different positions.

which ball is having the maximum mass? justify your answer

1. yellow ball
2. red ball
3. green ball