Chapter 12: Extending Surface Area and Volume
Prism
A solid figure that has two congruent, parallel polygons as its bases. Its sides are parallelograms
Pyramid
A solid shape with a polygon as a base and triangular faces that come to a point (vertex)
Cylinder
A solid shape with one curved surface and two congruent circular bases.
Cone
A three dimensional shape with a circular base and a vertex opposite of the base
Hemisphere
Half of a sphere
Similar Solid Ratio Theorem
If two solids have a scale factor of a:b, then the ratio of their surface areas are a2:b2 and the volume ratio is a3:b3
Cavalieri's Principle
If two solids have the same height and the same cross-sectional area at every level, then they have the same volume
Lateral Area of a Cylinder
L= 2πrh, where r is the radius of a base and h is the height
Lateral Area of a Cone
L= πrl, r is the radius of the base and l is the slant height
Lateral Area of a Pyramid
L=1/2Pl (l=slant height) and P is the perimeter of the base
Lateral Area of a Prism
L=Ph where P is the perimeter of the base and h is the height
Surface Area of a Pyramid
S= 1/2Pl+B, P is the perimeter of the base, l is the slant height, and B is the area of the base
Surface Area of a Cylinder
S= 2πr²+2πrh, where r is the radius of a base and h is the height
Surface Area of a Cone
S= πrl+πr², r is the radius of the base and l is the slant height
Surface Area of a Prism
S=L+2B or S=Ph+2B where L is the lateral area and B is the area of the base
Surface Area of a Hemisphere
SA= 1/2(4πr²) + πr², r is the radius of the hemisphere
Surface Area of a Sphere
SA=4πr², r is the radius of the sphere
Congruent Solids
Solids that have congruent corresponding angles, edges, faces, and equal volumes
Similar Solids
Solids that have exactly the same shape, but not necessarily the same size. The ratios of their corresponding linear measures are equal
Sphere
The locus of points in space that are a fixed distance from a center of a sphere
Surface Area
The sum of all the areas of all the faces or surfaces that enclose a solid or the sum of all the areas of all surfaces of a solid.
Lateral Area
The sum of the areas of the lateral faces of a solid
Volume of a Hemisphere
V= 1/2(4/3πr³) or 2/3πr³, r is the radius of the hemisphere
Volume of a Pyramid
V=1/3Bh, B is the area of the base and h is the height of the pyramid
Volume of a Cone
V=1/3πr²h, r is the radius of the base and h is the height of the cone
Volume of a Sphere
V=4/3πr³, r is the radius of the sphere
Volume of a Prism
V=Bh, B is the area of the base and h is the height of the prism
Volume of a Cylinder
V=πr²h, r is the radius of the base and h stands for the height of the cylinder
