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Mind Map Overal Idea Content Speed Notes Quick Coverage Plane figure The figures which we can be drawn on a flat surface or that lie on a plane are called Plane Figure. Example – Circle, Square, Rectangle etc. Solid figures The 3D shapes which occupy some space are called Solid Figures. Example – Cube, Cuboid,… readmore
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The figures which we can be drawn on a flat surface or that lie on a plane are called Plane Figure.
Example – Circle, Square, Rectangle etc.
The 3D shapes which occupy some space are called Solid Figures.
Example – Cube, Cuboid, Sphere etc. (Scroll down the till the end of the page)
Volume
Space occupied by any solid shape is the capacity or volume of that figure. The unit of volume is a cubic unit.
The area of all the faces of the solid shape is its total surface area. The unit of surface area is a square unit.
The surface area of the solid shape after leaving the top and bottom face of the figure is called the lateral surface of the shape. The unit of lateral surface area is a square unit.
Cube is a solid shape having 6 equal square faces.
| Lateral surface area of a cube | 4s2 |
| Total surface area of a cube | 6s2 |
| The volume of a cube | s3 |
| Diagonal | √3 s, s = edge of the cube = side length of face of cube |
What is the capacity of a cubical vessel having each side of 8 cm?
Solution
Given side = 8 cm So, Volume of the cubical vessel = l3 = (8)3 = 256 cm3.
Cuboid is a solid shape having 6 rectangular faces at a right angle.
| Lateral surface area of a cuboid | 2h(l + b) |
| Total surface area of a cuboid | 2(lb + bh + lh) |
| Volume of a cuboid | lbh |
| Diagonal | l = length, b = breadth, h = height |
What is the surface area of a cereal box whose length, breadth and height is 20 cm, 8 cm and 30 cm respectively?
Given, length = 20 cm, breadth = 8 cm, Height = 30 cm
Total surface area of the cereal box = 2(lb + bh + lh)
= 2(20 × 8 + 8 × 30 + 20 × 30)
= 2(160 + 240 + 600)
= 2(1000) = 2000 cm2.
If we fold a rectangular sheet with one side as its axis then it forms a cylinder. It is the curved surface of the cylinder. And if this curved surface is covered by two parallel circular bases then it forms a right circular cylinder.
| Curved surface area of a Right circular cylinder | 2πrh |
| Total surface area of a Right circular cylinder | 2πr2 + 2πrh = 2πr(r + h) |
| The volume of a Right circular cylinder | πr2h |
| r = radius, h = height |
If a right circular cylinder is hollow from inside then it has different curved surface and volume.
| Curved surface area of a Right circular cylinder | 2πh (R + r) |
| Total surface area of a Right circular cylinder | 2πh (R + r) + 2π(R2 – r2) |
| R = outer radius, r = inner radius, h = height |
Find the Total surface area of a hollow cylinder whose length is 22 cm and the external radius is 7 cm with 1 cm thickness. (π = 22/7)
Given, h = 22 cm, R = 7 cm, r = 6 cm (thickness of the wall is 1 cm).
Total surface area of a hollow cylinder = 2πh(R + r) + 2π(R2 – r2)
= 2(π) (22) (7+6) + 2(π)(72 – 62)
= 572 π + 26 π = 598 π
= 1878.67 cm2
If we revolve a right-angled triangle about one of its sides by taking other as its axis then the solid shape formed is known as a Right Circular Cone.
| Curved surface area of a Right Circular Cone | πrl = πr[√(h2 + r2)] |
| Total surface area of a Right Circular Cone | πr2 + πrl = πr(r + l) |
| The volume of Right Circular Cone | (1/3) πr2h |
| r = radius, h = height, l = slant height |
A sphere is a solid shape which is completely round like a ball. It has the same curved and total surface area.
| Curved or Lateral surface area of a Sphere | 4πr2 |
| Total surface area of a Sphere | 4πr2 |
| Volume of a Sphere | (4/3) πr3 |
| R = radius |
If we cut the sphere in two parts then is said to be a hemisphere.
| Curved or Lateral surface area of a Sphere | 2πr2 |
| Total surface area of a Sphere | 3πr2 |
| Volume of a Sphere | (2/3) πr3 |
| r = radius |
If we have a metal piece of cone shape with volume 523.33 cm3 and we mould it in a sphere then what will be the surface area of that sphere?
Given, volume of cone = 523.33 cm3
Volume of cone = Volume of Sphere
Volume of sphere = 100 π cm3
125 = r3
r = 5
Surface area of a sphere = 4πr2
= 314.28 cm2.
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Mind Map Overal Idea Content Speed Notes Quick Coverage A quadrilateral has 10 parts – 4 sides, 4 angles and 2 diagonals. Five measurements can determine a quadrilateral uniquely. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Practical Geometry Five measurements can determine a quadrilateral uniquely. A quadrilateral can… readmore
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A quadrilateral has 10 parts – 4 sides, 4 angles and 2 diagonals. Five measurements can determine a quadrilateral uniquely. (Scroll down till end of the page)
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Practical Geometry
Five measurements can determine a quadrilateral uniquely.
A quadrilateral can be constructed uniquely if the lengths of its four sides and a diagonal is given.
A quadrilateral can be constructed uniquely if its two diagonals and three sides are
known.
A quadrilateral can be constructed uniquely if its two adjacent sides and three angles
are known.
A quadrilateral can be constructed uniquely if its three sides and two included angles
are given.
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Mind Map Overal Idea Content Speed Notes Quick Coverage Any process that involves the rearrangement of structure of the substance or conversion of reactants into products is defined as Chemical Reaction. For a Chemical Reaction to occur, the change can be observed in the form of – Content Study Tools Audio, Visual & […] readmore
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Any process that involves the rearrangement of structure of the substance or conversion of reactants into products is defined as Chemical Reaction.
For a Chemical Reaction to occur, the change can be observed in the form of –
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Any process that involves the rearrangement of structure of the substance or conversion of reactants into products is defined as Chemical Reaction.
For a Chemical Reaction to occur, the change can be observed in the form of –
Exothermic Reactions: Those reactions in which energy is released in the form of heat are called Exothermic Reactions.
Examples –
(1) All combustion reactions e.g.
CH4+ 2O2 —> CO2 + 2H2O + Heat
(2) Thermite reactions e.g.
2A1 + Fe2O3 —> 2Fe + Al2O3 + Heat
Combinations are generally exothermic in nature. The decomposition of organic matters into compost is an example of exothermic reaction.
Endothermic Reactions: Those reactions in which energy is absorbed are called Endothermic Reactions.
Examples –
also, the reaction of photosynthesis –
Zn + H2 SO4 → ZnSO4 + H2
Formation of Precipitate: When a soluble carbonate reacts with Barium, Barium Carbonate precipitate can be observed.
Some chemical reactions are characterised by a change in state.
The symbolic representation of chemical reaction using symbols and formulae is known as Chemical Equation. For this, reactants are written on the left hand side whereas products are written on the right.
A balanced chemical equation is the one where the number of atoms involved in reactants side is equal to number of atoms on product side.
Eq.1. Example of Balanced Chemical Equation
To show how to balance the equation, the following equation is used-
Fe + H2O → Fe3O4 + H2
Step 1: First of all, draw the boxes around each formula as shown below-
Step 2: Find out the number of atoms of each element. For Example, on reactant side, 1 for Fe, 2 H, and 1 O and on product side we have, 3 for Fe, 4 for O and 2 for H.
Step 3: Start to balance the equation with the compound having maximum number of atoms. While balancing does not alter the formula of the compound.
Step 4: One by one balance each element on reactant and product side.
Step 5: After balancing number of atoms on both the side of the equation, finally check the correctness of the balanced equation.
Step 6: then write the symbols of the physical state of reactants and products as shown below-
3Fe(s) + 4H2O (g) → Fe3O4 (s) + 4H2 (g)
This above equation represents the balanced equation.
The basic ionic form of the equation is-
Fe2+ + Cr2O72- → Fe3+ + Cr3+
Oxidation half reaction is-
Reduction half reaction is-
Use the reduction half method to balance the equation. Balance the atoms in each half of the reaction except H and O atoms.
Cr2O72- (aq) → 2 Cr3+(aq)
Add water molecules as the reaction is taking place in acidic solution. This is to balance the O atoms and hydrogen ions.
Cr2O72- (aq) + 14 H+(aq) → 2 Cr3+(aq) + 7H2O (I)
Then balance the charges in both half reactions.
Fe2+(aq) → Fe3+(aq) + e–
Cr2O72- (aq) + 14 H+ + 6e– → 2 Cr3+ + 7H2O
6 Fe2+(aq) → 6 Fe3+(aq) + 6e–
Two half of the equations are added to get the overall reaction
6Fe2+(aq) + Cr2O72-(aq) + 14H+(aq) → 6Fe3+(aq) + 2Cr3+(aq) + 7H2O (I)
Eq.2. Example of Combination Reaction
Reactions can be exothermic as well as endothermic. Exothermic reaction release heats and raises the temperature of the surroundings. For Example, Respiration is an example of exothermic reaction.
Eq.3. Example of Exothermic Reaction
Endothermic reaction involved the absorption of the heat and thus it cools the surrounding. The decomposition of dead organic material is an endothermic reaction.
Eq.4. Example of Decomposition Reaction
Eq. 5. Example of Displacement Reaction
Eq. 6. Example of Double Displacement Reaction
Eq.7. Example of Redox Reaction
Metals are prone to corrosion. It is a slow conversion of metals into some undesirable compounds. This occur may be due to reaction with oxygen, gases, acids etc. When irons reacts with atmospheric oxygen and moisture, a red layer is formed on the surface of the iron, this process is known as Rusting.
Eq. 8. Equation for Iron Rusting
When food containing fats and oils are exposed to the atmosphere, the oxidation of fat and oil occurs, this is known as Rancidity.
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Mind Map Overal Idea Content Speed Notes Quick Coverage In order to provide food for a large population – regular production, proper management and distribution of food is necessary. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Crop : When plants of the same kind are grown and cultivated… readmore
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In order to provide food for a large population – regular production, proper management and distribution of food is necessary. (Scroll down till end of the page)
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Crop : When plants of the same kind are grown and cultivated at one place on a large scale,
it is called a crop.
In India, crops can be broadly categorised into two types based on seasons – Rabi and Kharif crops. Sowing of seeds at appropriate depths and distances gives good yield.
Good variety of seeds are sown after selection of healthy seeds.
Sowing is done by seed drills.
Soil needs replenishment and enrichment through the use of organic manure introduction of new crop varieties.
Basic practices of crop production:
(i) Preparation of Soil: One of the most important tasks in agriculture is to
turn the soil and loosen it.
The process of loosening and turning of the soil is
called tilling or ploughing.
(ii) Sowing: Sowing of seeds at appropriate depths and distances gives good yield.
Good variety of seeds is sown after selection of healthy seeds. Sowing is done by seed
drills.
(iii) Adding Manure and Fertilisers Soil needs replenishment and enrichment through the use of organic manure and fertilisers.
Use of chemical fertilisers
fertilisers has increased tremendously with the introduction of new crop varieties.
Fertiliser: The inorganic compounds containing nutrients such as nitrogen, potassium and phosphorus. They are made in the factories.
Example: ammonium sulphate, potash, etc.
Manure: A natural substance prepared from decomposition of plant and animal wastes (cow dung, animal bones, dead leaves, dead insects and vegetable wastes) by t(he action of microbes.
iv) Irrigation : Supply of water to crops at appropriate intervals is called
irrigation. Method of Irrigation:
(a)Tradition methods of Irrigation: Moat, Chain pump, Dheki, Rahat.
(b) Modern methods of Irrigation: Sprinkler system, Drip
(v) Protection from Weeds: Weeding involves removal of unwanted and
uncultivated plants called weeds.
(vi) Harvesting: Harvesting is the cutting of the mature crop manually or by
machines.
(vii) Storage Proper storage of grains is necessary to protect them from pests
and microorganisms.
Harvested food grains normally contain more moisture than
required for storage.
Large scale of storage of grains is done in silos and granaries to
pest like rats and insects.
Farmers store grains in jute bags or metallic bins.
Food is also obtained from animals for which animals are reared.
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