Cuboid :

Length, breadth and height of a cuboid are l, b, h respectively.

(i) Area of vertical surfaces of a cuboid = 2(l + b) × h

Here we have considered only 4 surfaces into consideration.

(ii) Total surface area of a cuboid = 2(lb + bh + lh)

Here we have taken all 6 surfaces into consideration.

(iii) Volume of a cuboid = l × b × h

Cube :

If l is the edge of a cube,

(i) Total surface area of a cube = 6l²

(ii) Area of vertical surfaces of a cube = 4l²

(iii) Volume of a cube = l³

Cylinder :

Radius of cylinder is r and height is h.

(i) Curved surface area of a cylinder = 2πrh

(ii) Total surface area of a cylinder = 2πr(r + h)

(iii) Volume of a cylinder = πr²h

Terms related to a cone and their relation :

A cone is shown in the figure.

O is the centre of the circle which is the base of the cone.

Seg OB is the radius (r).

Seg OA is perpendicular to the radius at the point O. So AO is the perpendicular height (h) of the cone.

AB is the slant height (l) of the cone.

Δ AOB is a right angled triangle.

∴ by Pythagoras' theorem,

AB² = AO² + OB²

i.e. l ² = h² + r².

Surface area of a Cone :

A cone has two surfaces. (i) Circular base (ii) Curved surface.

Area of the circular base = πr²      ......(1)

The curved surface area of the cone = πrl      .......(2)

The total surface area of the cone = curved surface area + area of the base

= πrl + πr²    …... [From (2) and (1)]

= πr[l + r]  

Volume of a Cone :

If the radii of the base and the heights of a cone and a cylinder are equal, then

3 x volume of the cone = Volume of cylinder = πr²h

∴ volume of the cone = $\frac{1}{3}$πr²h

Remember :

(i) Area of base of a cone = πr²   

(ii) Curved surface area of a cone = πrl

(iii) Total surface area of a cone = πr(l + r)  

(iv) Volume of a cone = $\frac{1}{3}$πr²h

Surface area and volume of a sphere :

Surface area of a sphere = 4 πr²

The volume of a sphere = $\frac{4}{3}$ πr³

Surface area of a hollow hemisphere = 2πr²

Total surface area of a solid hemisphere = surface area of a hemisphere + area of the circle = 2πr² + πr² = 3πr².

The volume of a hemisphere = $\frac{2}{3}$ πr³