wht all details can be given in a project for surface ,area&vol?

Question

like for verifying the formulas with innovative ideas.

Answer 1

not sure what yer askin

Answer 2

You could verify the volume of spheres, pyramids, cones, etc by filling a large jar with water to the brim and placing it in a pie plate.
Then gently immerse the object such as a golf ball into the jar. The water will overflow and go into the pie plate. Now pour the water into cylindrical can. You can measure the depth of the water and knowing the radius of the can, you can compute the volume of the spilled water, which should be equal to the volume of the object that was submerged. Use an object that will sink to the bottom and will be totally submerged. Don't use a ping pong ball as it will float.

Verifying surface area of solids is more difficult. I cannot think of a way to do it, unless you make cutouts that can be folded to form a cube, and then unfolded to show that there are indeed six faces and each is a square and so total surface area is 6s^2.

You could show that the area of a circle is smaller than the area of a regular polygon that circumscribes it and larger than the area of the regular polygon that the circle circumscribes. Then show how close the apothems come to being the radius of the circle as the number of sides of the regular polygons is increased towards infinity.