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SUBMITTED BY : shivani SURFACE AREAS AND VOLUMES SURFACE AREAS AND VOLUMES SURFACE AREAS AND VOLUMES

Surface area:

Definition of Surface Area Within our area section , we had to provide a definition for the meaning of area. That definition rested upon the square -- particularly a unit square. A unit Square can be 1" x 1" or 1 yd x 1 yd or 1 ft x 1 ft or a square by some other unit. Unit Square      We saw the area of a figure was nothing more than the sum of all unit squares of a figure. For the surface area of a solid, there is a similar definition, but it applies to the exterior surfaces of the solid. The definition of surface area is the sum of all unit squares that fit on the exterior of a solid Surface area

Surface Area of Prisms :

Surface Area of Prisms General Prism This is the best figure to begin with when investigating surface area. It is the most simple figure of all the solids. It is also a figure most people have personal experience due to either wrapping or opening gifts. All the surfaces of a prism are rectangular. This makes calculating the areas of these surfaces very easy to do. The area of rectangles have been discussed in another section, which is available for review before proceeding, if necessary. As the diagram below indicates, there are six surfaces to a rectangular prism. There is a front, back, top, bottom, left, and right to every rectangular prism. The surface are of a prism is nothing more than the sum of all the areas of these rectangles.

Surface Area of Cylinders:

Surface Area of Cylinders General Cylinder A cylinder has a total of three surfaces: a top, bottom, and middle. The top and bottom, which are circles, are easy to visualize. The area of a circle is πr 2 . So, the area of two circles would be πr 2 + πr 2 = 2πr 2 . The third surface, the lateral surface area, is less easy to visualize for the purposes of calculating its area, especially since it does not appear to be in a shape that fits a known area like a triangle or parallelogram . The surface being referred to is the curved wall of the cylinder.

Surface Area of Square Pyramids:

Surface Area of Square Pyramids General Pyramid      Pyramids that have a square base have a total of five surfaces. To determine the shapes of those surfaces, we will start with a pyramid from step one below. If we cut along the lateral edges of the pyramid, we can allow the figure to flatten out in step two below. From step two, the individual figures are easily identified as a square and four triangles.

volume:

volume Volume is how much three-dimensional space a substance (solid, liquid, gas, or plasma) or shape occupies or contains,[1] often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container, i. e. the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces. Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, and circular shapes can be easily calculated using arithmetic formulas. The volumes of more complicated shapes can be calculated by integral calculus if a formula exists for the shape's boundary. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space.

Volume of Prism:

Volume of Prism The volume V of any right prism is the product of B , the area of the base, and the height h of the prism. Formula: V = Bh

pyramid:

pyramid A pyramid is a polyhedron with a single base and lateral faces that are all triangular.  All lateral edges of a pyramid meet at a single point, or vertex . Pyramid Volume Theorem The volume V of any pyramid with height h and a base with area B is equal to one-third the product of the height and the area of the base. Formula: V = (1/3)Bh

Cylinder:

Cylinder Cylinder Volume Theorem The volume V of any cylinder with radius r and height h is equal to the product of the area of a base and the height. Formula: V = (PI)r 2 h

Cone:

Cone Cone Volume Theorem The volume V of any cone with radius r and height h is equal to one-third the product of the height and the area of the base. Formula: V = (1/3)(PI)r 2 h

Important Formulas of cone prism, cylinder, pyramid, ellips :

Important Formulas of cone prism, cylinder, pyramid, ellips cube = a 3 rectangular prism = a b c irregular prism = b h cylinder = b h = pi r 2 h pyramid = (1/3) b h cone = (1/3) b h = 1/3 pi r 2 h sphere = (4/3) pi r 3 ellipsoid = (4/3) pi r 1 r 2 r 3

CONE:

CONE

CYLINDER:

CYLINDER

ELLIPSE:

ELLIPSE

LENGTH OF AN ARC FORMULA:

LENGTH OF AN ARC FORMULA

PRISM:

PRISM

PYRAMID:

PYRAMID

SECTOR:

SECTOR

Slide 21:

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