allnic

alni318 Link to Chapter 9: Chapter 7.1

• Surface Area and Volumes Formulas: The surface area, S, and volume, V, of a right rectangular prism with length, &, width and height, h, are... S = 2&w + 2wh and V = &wh Rectangle The surface area, S, and volume, V, of a cube with side s are... S = 6s² and V = s³ CUBE

Chapter 7.2

• Altitude: An altitude of a prism is a segment that has endpoints in the planes contaiining the bases and that is perpendicular to both planes.

• Height: The height of s prism is the length of the altitude.

• Surface Area of a Right Prism: The surface area, S, of a right prism with lateral area L, base area, B, perimeter p, and the height h is S = L + 2B or S = hp + 2B

• Cavalieri's Principle: If two solids have equal heights and the cross sections formed by every plane parallel to the bases of both soilds have equal areas, then the two soilds have equal volumes. The Man Himself.

• Volume of a Prism: The volume, V, of a prism with height h and base area B is... V = Bh

Prism

Chapter 7.3

• Pyramids: A pyramid is any three-dimensional structure where the upper surfaces are triangular and come together at one point. The base of pyramids are generally any polygon shape. meaning that a pyramid usually has three or four sides. Otherwise known as lateral faces.

Pyramid

• Lateral faces: Are triangles that share a single vertex, called the VERTEX OF THE PYRAMID. Each lateral face has one edge in common with that base, called a BASE EDGE. The intersection of two lateral faces is a LATERAL EDGE.

• Altitude of a pyramid: Is the perpendicular segment from the vertex to the plane of the base. and the height of a pyramid is the length of its altitude.

• REGULAR PYRAMID: In a regular pyramid the base is a regular polygon and the lateral faces are equal triangles. The altitude of a pyramid is the perpendicular distance from the vertex to the base, which intersects the base center. The length of an altitude of a lateral face of a regular pyramid is called that SLANT HEIGHT of the pyramid.

• Surface Area of a Regular Pyramid: - The surface area, S, of a regular pyramid with lateral area L, base area B, perimeter of the base p, and the slant height & is... S = L + B or S = 1/2 &p + B

• Volume of a pyramid The volume of a pyramid is equal to one third the product of the altitude and the area of the base. The volume V, of a pyramid with height h, ad the base area B is... V=1/3Bh

Chapter 7.4

• Cylinders: A CYLINDER is a soild that consist of a circular region and its translated image on a parallel planes, with a LATERAL SURFACE connecting the cricles. The faces formed by the circular region and its translated image are called theBASES of the cylinder. An ALTITUDE of a cylinder is a segment that has endpoints in the planes containing the bases and is perpendicular to both planes The HEIGHT of a cylinder is the length of a altitude. The AXIS of a cylinder is a the segment joining the centers of the two bases. If the axis of a cylinder is perpendicular to the bases, then the cylinder is a RIGHT CYLINDER. If not, it is an OBLIQUE CYLINDER.

Cylinder

• Surface Area of a Right Cylinder: The surface area, S, of a right cylinder with lateral area L, base area B, radius r, and height h is... S = L+2B or S = 2rh + 2 (3.14 )r²

• Volume or a Cylinder: - The volume, V, or a cylinder with the radius r, height h, and the base area B is... V=Bh or V(3.14)r³

Chapter 7.5

• Cone: a cone is a three-dimensional figure that consists or a circular base and a curved lateral surface that connects the base to a single point not in the plane of the base, called a vertex. The altitude of a cone is the perpendicular segment from the vertex to that plane of the base. The height of the cone is that length of the altitude. If the altitude or a cone intersects the case of the cone at its center, the cone is a right cone. If, not. its an oblique cone.

• Surface Area of a Right Cone: The surface area, S, of a right cone with lateral area, L, base of area, B, and the radius, r, and slant & is... S = L+B or S = (3.14) r&+ (3.14)r².

• Volume of a Cone: The voulme, V, of a cone with radius r, height h, and base area B is... V= ¹/³ Bh or V= ¹/³ (3.14) r²h. Cone

Chapter 7.6 Sphere • Volume of a Sphere: The volume, V, of a sphere with radius r is... V = 4/3 (3.14)r³.

• Surface Area or a Sphere: The surface area, S,of a sphere with a radius r is... S - 4 (3.14) r².

Sphere

Extra:

1. Find the volume of a triangular prism with a length of 3, a height of 6, and a width of 4.

1/2 x 3 x 4 x 6 =