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Tuesday, 29 April 2014

SURFACE AREA AND VOLUME

A PRISM is a solid whose cross sectional area is the same all along its length, and all its sides are flat.

In a RIGHT PRISM the edges of the sides are perpendicular to the base. If the sides are not perpendicular to the base it is an OBLIQUE PRISM.

A COMPOSITE SOLID is one which is made up of two or more solids (e.e. a cube and a hemisphere stuck together).

The APEX of a pyramid or cone is the very top point (vertex).

A RIGHT PYRAMID is one which has its apex aligned directly above the center of the base. The surface area of a pyramid comprises the area of the sides plus the base (unless stated otherwise).

The surface area of a closed (right) cylinder is SA=2\pi r^2+2\pi rh\quad\quad\quad \mbox{CLOSED CYLINDER} where h=height, r=radius of the base.

A RIGHT CONE is one which has its apex aligned directly above the center of the base. The surface area of a right cone is 

SA=\pi r l+\pi r^2\quad\quad\quad \mbox{RIGHT CONE} where l=
slant height, r=radius of the base.

A SPHERE is a surface whose shape is the outside of a ball.\\ The surface area of a sphere of radius r is SA=4\pi r^2\quad\quad\quad \mbox{SPHERE}

The surface area of composite solids involving a sphere and other solids excludes common areas (unless stated otherwise)\\ The volume of a right prism is V=Ah \quad\quad\quad \mbox{RIGHT PRISM} where h=height of the prism, and A=cross-sectional area.

The volume of a cylinder is V= \pi r^2 h\quad\quad\quad \mbox{CYLINDER} (really same as V=Ah where A=\pi r^2 here.)

The volume of a sphere of radius r is V={4\pi r^3 \over 3 }\quad\quad\quad \mbox{SPHERE}

The volume of a pyramid is V={1\over 3} Ah\quad\quad\quad \mbox{PYRAMID} where h=perpendicular height, A=area of base.

The volume of a cone is V={1\over 3} \pi r^2 h\quad\quad\quad \mbox{CONE} (really same as {1\over 3}Ah where A=\pi r^2 here.)

Volume of composite solids is the sum of its volume parts. Conversion between volume and capacity: 1 m^2=1 kL, 1 cm^2=1 mL,1 L =1000 mL

AREAS OF SIMILAR FIGURES ARE RELATED:

If the matching sides of two similar figures are in the ratio m:n then the areas are in the ratio m^2:n^2.

So if you double the sides of a figure its area becomes 4 (since 2^2=4) times bigger.

VOLUMES OF SIMILAR FIGURES ARE RELATED:

If the matching sides of two similar figures are in the ratio m:n then (1) the ratio of their surface areas is m^2:n^2.

(2) the ratio of their volumes is m^2:n^2. So if you double the sides of a figure its volume becomes 8 (since 2^3=8) times bigger.

PYTHAGORAS' THEOREM applies to right angled triangles: a^2+b^2=c^2 where the longer side is c. This is useful when finding some surface areas and volumes for pyramids where right angled-triangles can occur. }

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