0i. Plane Figure:
Plane figure are the figure which lies in a plane or to put it simply which we can draw on a piece of paper
Example: Triangle, circle, quadilateral, etc
ii. Solid Figure:
Solid figure does not lie in a single plane.They are three dimensional figure
Example: Cube, Cylinder, Sphere.
iii. Mensuration:
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It is branch of mathematics which is concerned about the measurement of length ,area and Volume of plane and Solid figure
iv. Perimeter:
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The perimeter of plane figure is defined as the length of the boundary.
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It units is same as that of length i.e. m, cm, km.
1 Meter | 10 Decimeter | 100 centimeter |
1 Decimeter | 10 centimeter | 100 millimeter |
1 Km | 10 Hectometer | 100 Decameter |
1 Decameter | 10 meter | 1000 centimeter |
v. Surface Area or Area:
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The area of the plane figure is the surface enclosed by its boundary
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It unit is square of length unit. i.e. m2, km2
1 square Meter | 100 square Decimeter | 10000 square centimeter |
1 square Decimeter | 100 square centimeter | 10000 square millimeter |
1 Hectare | 100 squareDecameter | 10000 square meter |
1 square myraimeter | 100 square kilometer | 108 squaremeter |
vi. Volume:
1 cm3 | 1mL | 1000 mm3 |
1 Litre | 1000mL | 1000 cm3 |
1 m3 | 106 cm3 | 1000 L |
1 dm3 | 1000 cm3 | 1 L |
vii. 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 |
Diagonal of the cuboids | (L2+B2+H2)1/2 |
Volume of a cuboids | LBH |
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 | |
Volume of a cube | L3 |
viii. 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 | π r2h |
ix. 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 centre 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)πr 2h |
x. Surface Area and Volume of sphere and hemisphere:
Sphere | A sphere can also be considered as a solid obtained on rotating a circle About its 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 a 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 | (4/3)πr 3 |
Curved Surface area of hemisphere | 2πr2 |
Total Surface area of hemisphere | 3πr2 |
Volume of hemisphere | (2/3)πr 3 |
Volume of the spherical shell whose outer and inner radii and ‘R’ and ‘r’ respectively | (2/3)π(R3-r3) |
xi. How the Surface area and Volume are determined
Area of Circle | The circumference of a circle is 2πr. This is the definition of π (pi). Divide the circle into many triangular segments. The area of the triangles is 1/2 times the sum of their bases, 2πr (the circumference), times their height, r.A=(1/2)2πrr=πr2 |
Surface Area of cylinder | This can be imagined as unwrapping the surface into a rectangle. |
Surface area of cone | This can be achieved by divide the surface of the cone into its triangles, or the surface of the cone into many thin triangles. The area of the triangles is 1/2 times the sum of their bases, p, times their height,A=(1/2)2πrs=πrs |
