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: $$1 m^3=1 kL $$ $$ 1 cm^3=1 mL $$
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 $m^3:n^3$. 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. }
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: $$1 m^3=1 kL $$ $$ 1 cm^3=1 mL $$
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 $m^3:n^3$. 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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