Perimeter:
The perimeter of plane figure is defined as the length of the boundary.
Its units is same as that of length i.e., m, cm, km
Area:
The area of the plane figure is the surface enclosed by the boundary.
Its unit is square of length unit i.e., m2, km2
Volume:
Volume is the measure of the amount of space inside of a solid figure, like a cube, ball, cylinder or pyramid.
Its units are always “cubic”, that is the number of little element cubes that fit inside the figure.
Volume Unit Conversion:
| 1 cm3 | 1 mL | 1000 mm3 |
| 1 litre | 1000 mL | 1000 cm3 |
| 1 m3 | 106 cm3 | 1000 L |
| 1 dm3 | 1000 cm3 | 1 L |
Surface Area and Volume of Cube and Cuboid
| Type | Measurement |
| Surface Area of Cuboid of Length L, Breadth B and Height H | 2(LB + BH + LH) |
| Lateral surface area of the cuboids | 2(L + B)H |
| Diagonals of the cuboids | √(L2 + B2 + H2) |
| Volume of a cuboids | L x B x H |
| Length of all 12 edges of the cuboids | 4(L + B + H) |
| Surface Area of Cube of side L | 6L2 |
| Lateral surface area of the cube | 4L2 |
| Diagonal of the cube | L√3 |
| Volume of a cube | L3 |
Surface Area and Volume of Right Circular cylinder
Radius: The radius (r) of the circular base is called the radius of the cylinder.
Height: The length of the axis of the cylinder is called the height (h) of the cylinder.
Lateral surface: The curved surface joining the two base of a right circular cylinder is called Lateral surface.
| Type | Measurement |
| Curved or Lateral Surface Area of cylinder | 2πrh |
| Total Surface area of cylinder | 2πr(h + r) |
| Volume of Cylinder | πr2h |
Surface Area and Volume of Right Circular Cone
Radius: The radius (r) of the circular base is called the radius of the cone.
Height: The length of the line segment joining the vertex to the center of base is called the height (h) of the cone.
Slant Height: The length of the segment joining the vertex to any point on the circular edge of the base is called the slant height (L) of the cone.
Lateral Surface Area: The curved surface joining the base and uppermost point of a right circular cone is called Lateral Surface.
| Type | Measurement |
| Curved or Lateral Surface Area of cone | πrL |
| Total surface area of cone | πr(L + r) |
| Volume of Cone | 1/3 πr2h |
Surface Area and Volume of sphere and hemisphere
Sphere: A sphere can also be considered as a solid obtained on rotating a circle about the diameter.
Hemisphere: A plane through the centre of the sphere divides the sphere into two equal parts, each of which is called a hemisphere.
Radius: The radius of the circle by which it is formed.
Spherical Shell: The difference of two solid concentric spheres is called spherical Shell.
Lateral Surface Area for Sphere: Total surface area of the sphere.
Lateral Surface Area of Hemisphere: It is the curved surface area leaving the circular base.
| Type | Measurement |
| Surface Area of Sphere | 4πr2 |
| Volume of Sphere | 4/3πr3 |
| Curved Surface Area of hemisphere | 2πr2 |
| Total Surface Area of hemisphere | 3πr2 |
| Volume of hemisphere | 2/3πr3 |
| Volume of the spherical shell whose outer and inner radii are ‘R’ and ‘r’ respectively | 4/3π(R3 – r3) |
Surface Area and Volume of frustum of cone:
h = vertical height of the frustum
l = slant height of the frustum
r1 and r2 are radii of the two bases (ends) of the frustum.
| Type | Measurement |
| Volume of a frustum of a cone | 1/3πh(r12 + r22+ r1r2) |
| Slant height of frustum of a cone | √[h2 + (r1 – r2)2] |
| Curved surface area of a frustum of a cone | π(r1 + r2)l |
| Total surface area of frustum of a cone | π(r1 + r2)l + πr12 + πr22 |