# what is the volume and total surface area of: cube,cuboid,pyramids and cones???plz also show the derivations of each formulae

sciencesolve | Certified Educator

You should remember that the total surface area of a cube is the sum of areas of its six faces such that:

`TSA = 6(l*l) =gt TSA = 6l^2`

Notice that the areas of the six faces of the cube are all equal to `l^2` , hence the `TSA = 6l^2` .

You should remember that the total surface area of a cuboid is the sum of areas of its six faces such that:

`TSA = 2l*w + 2l*h + 2*w*h`

Notice that l,w,h represents the length, width and height of cuboid.

You should remember that the total surface area of a pyramid with rectangular base is the sum of areas of its four faces + the area of the base such that:

TSA = Area of base + 2*Area of triangular faces (base of triangle is the length of rectangular base) + 2*Area of triangular faces (base of triangle is the width of rectangular base)

You should remember that the total surface area of a pyramid with square base is the sum of areas of its four faces + the area of the base such that:

TSA = Area of base + 4*Area of triangular faces

You should remember that the total surface area of a cone  is the sum of the area of the base + area of curved surface such that:

`TSA = pi*r^2 + pi*r*s`