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__**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

**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.

• 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 [|Pyramids]

__**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 the**__BASES__** 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. [|Right and Oblique Cones]

__**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.