Surface Areas and Volumes of Combinations of Solids
* Complex solid shapes are composed of fundamental solid shapes.
* By summing the surface areas of the simpler shapes that compose a complex shape, you can calculate a area of a complex shape.
* By summing the volumes of the simpler shapes that compose a complex shape, you can calculate the volume of a complex shape.
* For solving the problems involving the areas and volumes of complex shapes, you need to remember the standard formulae used for simple shapes.
Conversion of Solid from One Shape to Another
* Problems is converting solids from one shape to another are solved by equating volumes.
* Problems are solved by evaluating a variable in the equality of volumes equation.
* The variable to be determined is either a available number of objects of the converted solid, or it is some dimension of the converted sold.
* The surface area of a combination of solid may be evaluated by finding dimension of the new solid, and calculating the surface area.
* Problems involving flow rates can be solved by equating volumes and evaluating for a missing variable.
Frustum of a Cone
* When we cut a right circular cone with a plane parallel to the base of the cone, then the solid shapes between the plane and the base of the cone is called frustum of the cone.
* The curved surface area of a frustum of a cone = πɭ = ( r_{1} + r_{2} )
Where,
ɭ = \sqrt{h² + ( r_{1} - r_{2} )²}
* The total surface area of a frustum of a cone = πɭ ( r_{1} + r_{2} ) + πr_{1}² +πr_{2}²
Where,
ɭ = \sqrt{h² + ( r_{1} - r_{2} )²}