Place the plywood sheet on a table. Measure the diameter of the sphere you wish to carve or grind. Mark the halfway point on this line. Hammer the nail on this spot. Attach one end of a string (half the length of the total diameter) to the nail and the other end to a pencil.
Pull the string with the pencil so that it is taught and at the correct position; then pull it around the nail, drawing a circle on the plywood. Use a jigsaw to cut out the circle from the plywood. This shape will be your template so that you can grind the spherical shape.
Cut out a second piece, identical to the first, and cut it in half, so that each piece is a semicircle. Place the half-piece on the sphere you wish to grind to check its shape. The template will immediately indicate any bumps or disproportionate areas on its surface. Guide the template along the exterior and grind off any bumps until the template is a snug fit with the surface.
Continue checking around the entire sphere using this method until the sphere gets round. Be careful not to grind off too much at any point as this reduction will offset the entire proportion of the sphere. Work carefully and remove only the highest points as necessary.
Place the template on random spots on the sphere to check its shape. As a final test, place the sphere in the complete ring of plywood. The sphere should easily fit, and turn within it. Wherever it jams is a spot that need further grinding. Continue grinding until the sphere moves freely in all directions.