(i) Area
of the circle = pr^{2}
where r is the radius of the circle. Circumference = 2pr .

(ii) Sector of a circle. Length of arc = x 2pr

Area = x pr^{2} where q is the angle of the sector in degrees and r
is the radius of the circle.

Area = (1/2)1r; 1 is length of arc and r is radius. .

(iii) Ring:
Ring is the space enclosed by two concentric circles. Area = pR^{2} - pr^{2} = p(R + r) (R - r) where R is the radius of the outer circle and r is
the radius of the inner circle. .

Area = p ab where “a” is semi-major axis and “b” is semi-minor axis. Perimeter = p (a + b) .

Solids are three-dimensional objects which, in addition to areas, have volumes also. For solids, two different types of areas are defined .

(a) Lateral surface area or curved surface area and

(b) Total surface area

As the name itself indicates, lateral surface area is the area of the LATERAL surfaces of the solid. Total surface area includes the areas of the top and the bottom surfaces also of the solid. Hence, Total surface area = Lateral surface area + Area of the top face + Area of the bottom face. .

In solids (like cylinder, cone, sphere) where the lateral surface is curved, the lateral surface area is usually referred to as the “curved surface area.” .

For any solid, whose faces are regular polygons, there is a definite relationship between the number of vertices, the number of sides and the number of edges of the solid. This relationship is given by “Euler’s Rule”. .

Number of faces + Number of vertices

= Number of edges + 2 (Euler’s Rule)

A right prism is a solid whose top and bottom faces (bottom face is called base) are parallel to each other and are identical polygons (of any number of sides) that are parallel. The faces joining the top and bottom faces are rectangles and are called lateral faces. There are as many lateral faces as there are sides in the base. The distance between the base and the top is called height or length of the right prism. .

In a right prism, if a perpendicular is drawn from the centre of the top face, it passes through the centre of the base. .

For any prism,

Lateral Surface Area = Perimeter of base x Height of the prism

Total Surface Area = Lateral Surface Area + 2 x Area of base

Volume = Area of base x Height of the prism

A right prism whose base is a rectangle is called a rectangular solid or cuboid. If 1 and b are respectively the length and breadth of the base and h, the height, then .

Volume = lbh

Lateral Surface Area = 2(1 + b) . h .

Total Surface Area = 2(1 + b)h + 2lb = 2(lb + lh + bh)

Longest diagonal of the cuboid =