Surface Area

Volume and Surface Area

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Volume and Surface Area

Volume

Volume is the amount of three-dimensional space an object occupies, in cubic units, within a container.
Volume and Unit Cubes:
Volume is measured in cubic units. Think in three-dimensions.
The volume of an object can be represented by the number of unit cubes that can be placed within the object.
Volume and Surface Area 1
For some figures, the unit cubes fit “nicely” into the object, while other objects hold fractional parts of a unit cube.
The volume of this rectangular prism (“box”) is the total of the number of unit cubes it holds. There are a total of 16 unit cubes within the solid.
Volume and Surface Area 2
The volume = 16 cubic units

Volume as Area times Depth:
While counting the number of unit cubes within the rectangular prism,
a pattern can be seen that will help to determine the count of the cubes quickly.
Pattern: Find the number of cubes seen in one face and multiply times the number of rows of that face, going to the back of the figure.
Volume and Surface Area 3
Volume = (cubes in face) • (rows going back)
= 8 • 2 = 16 square units
Pattern: A pattern similar to that shown above can be expressed using the term “area”. The number of cube faces seen in the face of the figure, comprise the area of the face of the figure. The new pattern is expressed as:
Volume and Surface Area 4
Volume = (area of face) • (depth of face)
= (4 • 2) • 2 = 16 square units

This will be a popular strategy to determine the volume of many solids.
This pattern utilizes a “limiting argument” with the area being a 2-dimensional cross section with no thickness. The thickness, however, can be theoretically considered very, very, very small so as not to affect calculations. These cross sections are stacked to the height of the figure, creating the formula V = B • h, with B the area of the base and h = height.
(In the example about consider the area of the face to be the base, and the depth to be the height; just tip it over.)

Surface area

Surface area is the total area that the surface of a three-dimensional object occupies, in square units.

Surface Area using a Net:
If you cut apart this box and flatten out the pieces, you will get a shape similar to the one at the right, called a net.
Several options are possible.
Volume and Surface Area 5
The advantage of examining the net is that you can see each of the faces of the figure, making computing the surface area easier.

Volume and Surface Area 6
The surface area of this rectangular prism will be the sum of areas of all six shapes in the net.
Surface Area = (2•2) + (2•4) + (2•4) + (2•4) + (2•4) + (2•2) = 40 square units.

Working with different units:

  • 1 square foot = 144 square inches
    (a square foot is 1 ft. by 1 ft. which is also 12 in. by 12 in.)
  • 1 cubic foot = 1728 cubic inches
    (a cubic foot is 1 ft. by 1 ft. by 1 ft. which is also 12 in. by 12 in. by 12 in.)
  • 1 cubic yard = 27 cubic feet
    (a cubic yard is 1 yd. by 1 yd. by 1 yd. which is also 3 ft. by 3 ft. by 3 ft.)

Formulas:

Volume and Surface Area 7 Volume and Surface Area 8

What is meant by Sublimation and what are the Factors that Affect the Rate of Evaporation

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What is Sublimation in chemistry

Sublimation : The changing of a solid directly into vapours on heating, and of vapours into solid on cooling, is known as sublimation.
Sublimation can be represented as:
What is meant by Sublimation and what are the Factors that Affect the Rate of Evaporation 1 The solid substance which undergoes sublimation is said to ‘sublime’. the solid obtained by cooling the vapours of the solid is called a ‘sublimate’.
What is meant by Sublimation and what are the Factors that Affect the Rate of Evaporation 2Ex.       When solid ammonium chloride is heated, it directly changes into ammonium chloride vapour. And when hot Ammonium chloride vapour is cooled, it directly changes into solid ammonium chloride. Ammonium chloride, Iodine, Camphor, Naphthalene and Anthracene.

Evaporation : The process of change of a liquid into vapour at any temperature below its boiling point is called evaporation.

Factors affecting evaporation :

  1. Temperature : Rate of evaporation increase with increase in temperature. This is because with the increase in temperature more number of particles get enough kinetic energy to go into the vapour state.
    Ex.       Drying of clothes take place rapidly in summer than in winter
  2. Surface Area : The rate of evaporation increases on increasing the surface area of the liquid
    Ex.       If the same liquid is kept in a test tube and in a china dish, then the liquid kept in the china dish will evaporate more rapidly : Because more of its surface area is exposed to air.
  3. Humidity : Humidity is the amount of water vapour present in air. Air around us cannot hold more than a definite quantity of water vapour at a given temperature. If the amount of water in air is already large i.e., humidity is more, the rate of evaporation decreases. Thus, the rate of evaporation increases with decrease in humidity in the atmosphere.
    Ex.       Drying of clothes on a humid day.
  4. Wind speed :   The rate of evaporation also increases with increase in speed of the wind. This is because with increase in speed of wind, the particles of water vapour move away with wind resulting decrease in the amount of vapour in the atmosphere.
    Ex.       Clothes dry faster on a windy day.