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Area for rectangles is simply how many squares fit in the space. If it's 3 units long and 4 units high, that's 4 stacks of 3 squares or 12 (3x4) square units

Area for a circle is pi times the radius squared. So a circle with the radius of 3 units has an area of 3x3x3.14 units. (I could also tell you diameter in which case you'd have to chop it in half first to get radius)

Volume is how many cubes of a certain size fit inside a solid. A box that is 3x4 on the bottom has 12 cubes that will fit on "the first floor". If the box is 10 high, then there are 120 (3x4x10) cubic units inside the box

Figuring out the number of cubes inside of a sphere (a ball) would be difficult. However someone figured out the formula for this is 4/3pi r cubed. So if a sphere had a radius of 10, the volume would be 4 / 3 x 3.14 x 10 x 10 x 10 or approximately 4186.67 cubic units