mildam

MiDa118th

Chapter 7

KEY
 * S**: Surface Area, **V**: Volume, **l**: length, **w**: width, **h**: height, **s**: side, **L**: lateral area, **B**: base area, **p**: perimeter, **r**: radius


 * 7.1 Surface Area and Volume**

S and V of a right rectangular prism with l, w, and h are:

S =2lw + 2wh + 2lh, and V= lwh

S and V of a cube with s are: S =6s^2, and V= s^3




 * 7.2 Surface Area and Volume of a Prism**

Altitude: A segment that has end point in the planes containing the bases and is perpendicular to both planes.

Height: The length of an altitude

S of a right prism with L, B, p, h is:

S =L + 2B or S= hp + 2B

Cavalieri’s Principle: If 2 solids have equal heights and the cross sections formed by every plane parallel to the bases of both solids have equal areas, then the 2 solids have equal volumes.

V of a prism with h and B is:

V = Bh




 * 7.3 Surface Area and Volume of Pyramids**

Pyramid: A polyhedron consisting of a base (Polygon) and 3 or more lateral faces.

Base: The bottom polygon of a pyramid.

Lateral Faces: The slanting faces of the pyramid.

Vertex of the Pyramid: The highest point of the pyramid. Base Edge: Where the lateral face meets the base.

Lateral Edge: Intersection of 2 lateral faces.

Regular Pyramid: A pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles.

Slant Height: The altitude of a lateral face of a regular pyramid.

S of a regular pyramid with L, B, p of base, l is:

S =L + B or S= 1/2lp + B

V of a pyramid with h, and B is:

V = 1/3Bh




 * 7.4 Surface Area and Volume of Cylinders**

Cylinder: A solid that consists of a circular region and its translated image on a parallel plane.

Bases: Faces formed by the circular region and its translated region.

Altitude: A segment that has endpoints in the planes containing bases and is perpendicular to both planes.

Height: The length of the altitude

Axis: The segment joining the centers of the 2 bases

Right Cylinder: The axis is perpendicular to the bases

Oblique Cylinder: The axis s not perpendicular to the bases

S of a right cylinder with L, B, r, and h is:

S =L + 2B or S= 2 x 3.14rh + 2 x 3.14r^2

V of a cylinder with r, h, and B is:

V =Bh or V= 3.14 x r^2h




 * 7.5 Surface Area and Volume of Cones**

Cone: 3 dimensional figure that consists of a circular base and a curved lateral surface that connects the base to a single point not in the vertex

Vertex: The highest point of the cone or the lowest point of the cone.

Right cone: The altitude of a cone intersects the base of the cone at its center.

Oblique cone: The altitude of a cone doesn’t intersect the base of the cone at its center

S of a right cone with L, B, r, and l is:

S =L + B or S= 3.14 x rl + 3.14 x r^2

V of a cone with r, h, and B is:

V =1/3 x Bh or V= 1/3 x r^2h




 * 7.6 Surface Area and Volume of Spheres**

Sphere: A set of all points in space that are same distance from a given point known as the center of the sphere.

Annulus: The ring shaped figure.

V of a sphere with r is:

V = 4/3 x 3.14r^3

S of a sphere with r is:

S = 4 x 3.14r^2

1. B =2 x 3 h= 7 V = Bh

V =3 x 7 V= 21u^3

2. h =7 p= 30 S = hp + 2B

B =2 x 3 S= 7 x 30 + 6 S = 216

3. B =25 h= 29.68

V =1/3 x 25 x 29.68 V= 247.3

4. l =16 p= 20 B = 25

S =1/2 x 16 x 20 + 25 S= 125 u^2

5. r =8 h= 20 S = 2 x 3.14 x 8 x 20 + 2 x 3.14 x 8^2

S = 1407.43