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