The figure of a square sheet of paper is shown below. Length of one side of the paper is 36 centimetres and AB=10 centimetres. The shaded portion is cut and folded into a square pyramid.

What is the length of the base edge of the pyramid?

A cube is a three-dimensional figure as shown in Fig. It has six faces and all of them are identical squares. The length of an edge of the cube is given by l. Find the formula for the total length of the edges of a cube.

Shazli took a wire of length 44cm and bent it into she shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Take pi=22/7)

A square metal wire loop of side 0.10 m and resistance 1 Omega is moved at a constant velocity nu_0 in a uniform magnetic field of induction B=2 Wb m^(-2) as shown in the figure . The magnetic field lines are bot to the plane of the loop directed into the paper. The loop is connected to a network of resistors each of value 3 Omega . The resistance of lead wires OS and PQ are negligible . what should be the speed nu_0 of the loop so as to have a steady current of 1mA in the loop ? Also indicate the direction of current in the loop .

A rectangular sheet of tin 45 cm by 24 cm is to made into a box without top, by cutting-off square from each other corner and folding up the flaps. What should be the side of the square to be cut-off so that the volume of the box is maximum?

A kite in the shape of a square with diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to made of three different shades as showing in fig . How much paper of each shade has been used in it ?

Pragya wrapped a cord aroud a circular pipe of radius 4cm (adjoining figure) and cut of the length required of the cord. Then she wrapped it around a square box of side 4 cm (also shown). Did she have any cord left? (pi=3.14)