schnat

ScNa228 chapter 9 link //-7.1 Surface Area and Volume//
 * Chapter 7 Surface Area and Volume**

//**Objectives:**// 1. Explore ratios of surface area to volume 2. Develop the concepts of maximizing volume and minimizing surface area

__Right rectangular prism:__ Surface Area: S= 2lw + 2wh + 2lh Volume: V= lwh //(l=length,w=width,h=height)//
 * Surface area and volume formulas:**

-find the surface area of a rectangular prism. L=10inches W=5inches H=5inches
 * Example problem:**

2(10x5)+2(5x5)+2(10+5)=__**250inches²**__

-find the volume of a rectangular prism with a length of 5, height of 2 and width of 10. V=LWH 5x2x10=__**100 units³**__
 * Example problem:**

//__Cube:__// Surface Area: SA= 6s² Volume: V= s³ //(s=sides)//

[|Extra Practice] [|Surface area and volume simulator]

//-7.2 Surface Area and Volume of Prisms//
 * Chapter 7 Surface Area and Volume**

//**Objectives:**// 1.Define and use a formula for finding the surface area of a right prism. 2.Define and use a formula for finding the volume of a right prism. 3.Use Cavalieri's principle to develop a formula for the volume of a right or oblique prism.

-The **[|altitude]** of a prism is the segment that has endpoints in the planes that containes the bases and are perpendicular to each plane.
 * Vocabulary:**

-The **[|height]** of a prism is the length of the altitude.

S= L + 2B S= //hp// + 2B //(h=height,l=lateral area,b=base,p=perimeter)//
 * Surface Area of a Right [|Prism]**

[|**Cavalieri's Principle:**] If two solids have equal heights and the cross sections formed by every plane parallel to the bases of both solids have equal areas, then the two solids have equal volume.

V=B//h (b=base,h=height)//
 * Volume of a prism:**

//-7.3 Surface Area and Volume of Pyramids//
 * Chapter 7 Surface Area and Volume**

1.Define and use a formula for the surface area of a regular pyramid. 2.Define and use a formula for the volume of a pyramid.
 * //Objectives://**

-A **pyramid** is a polyhedron consisting of a base.
 * Vocabulary:**

-The **base** is a polygonal face that is opposite the vertex.

-The **lateral face** is the faces of a prism or pyramid that are not bases.

-**Vertex of a pyramid** is when all the lateral faces are triangles that share the same vertex.

-The **Base edge** is when each lateral face has one edge in common with the base.

-**Lateral edge** is the intersection of two lateral faces of a polyhedron.

-**Altitude** of a pyramid is the perpendicular segment from the vertex to the plane of the base.

-**Height** is the length of the altitude.

-A **regular pyramid** is a pyramid whose base is a regular polygon and whose lateral faces are congruent isosoceles triangles.

-The **slant height** is the length of an altitude of a lateral face of a regular pyramid.

S= L + B S= 1/2l//p// + B (L=lateral area,B=base area,p=perimeter of base,l=slant height)
 * Surface Area of a Regular Pyramid:**

V=1/3B//h// (B=base,//h//=height)
 * Volume of a pyramid:**

-A pyramid with a base edge of 400 and a height of 600, what would be the volume of the pyramid?** V= 1/3(400²)(600)=**32000000** The Volume of the pyramid is **32000000**.
 * Example problem:

//-7.4 Surface Area and Volume of Cylinders//
 * Chapter 7 Surface Area and Volume**

1.Define and use a formula for the surface area of a right cylinder. 2.Define and use a formula for the volume of a cylinder.
 * //Objectives://**

-A **cylinder** is a solid that consists of a circular region and its translated image on a parallel plane.
 * Vocabulary:**

-A **lateral surface** connects the surface of the two circles.

-The faces formed by the circular region and 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 ans its perendicular to both planes.

-The **height** of a cylinder is the length of an altitude.

-**Axis** of a cylinder is the segment joining the centers of the two bases.

-**Right cylinder** is when the axis of the cylinder is perpendicular to the bases.

-**Oblique cylinder** is when the axis of the cylinder is not perpendicular to the bases.

S= L + 2B S=2(pi)rh + 2(pi)r²
 * Surface Area of a Right Cylinder:**

V= B//h// V= (pi)r²//h//
 * Volume of a Cylinder:**

-if a penny has a diameter of 18.25 millimeters and a thinkness of about 1.25 millimeters what would be the surface area of the penny?
 * Example Problem:

(half the diameter is 9.125)**

S= 2(pi)rh + 2(pi)r² S= 2(pi)(9.125)(1.25) + 2(pi)(9.125)² = **594.84 square millimeters**

//-7.5 Surface Area and Volume of Cones//
 * Chapter 7 Surface Area and Volume**

1.Define and use the formula for the surface area of a cone. 2.Define and use the formula for the volume of a cone.
 * //Objectives://**

-**A **cone** is a three-dimensional figure that consists of a circular base and a curved lateral surface that connects the base to a single point not in the plane of the base
 * Vocabulary:

-A **Base** is a polygonal face that is opposite the vertex.

-The **Lateral Surface** is the curved surface of a cylinder or cone.

-**Vertex** is the point where the edges of a figure intersects.

-The **altitude** of a cone is the perpendicular segment from the vertex to the plane is the length of the base.

-The **height** of a cone is the length of the altitude.

-A cone is a **right cone** if the altitude of the cone intersects the base of the cone at its center.

-A cone is an **oblique cone** if the altitude of the cone does not intersect the base of the cone at its center.

S= L + B S= (pi)rl + (pi)r²
 * Surface Area of a Right Cone:**

V= 1/3B//h// V= 1/3(pi)r²//h//
 * Volume of a cone:**

-7.6 Surface Area and Volume of spheres
 * Chapter 7 Surface Area and Volume of Spheres**

1.Define and use the formula for the surface area of a sphere. 2.Define and use the formula for the volume of a sphere.
 * //Objectives://**

V= 4/3(pi)r³
 * Volume of a sphere:**

S= 4(pi)r²
 * Surface Area of a Sphere:**

[|**//Extra help for solving Surface Area and Volume problems//**]

1. A triangular prism has a height of 5 inches, and its base sides are 5,5,5 inches. -what is the volume? V=BH V=(30)(5)
 * V=150 inches³**

2. A triangular prism has a height of 4 inches, the base sides are 3,8,5 inches. -what is the Surface area? S.A=HP+2B S.A=(4)(15)+2(32)
 * S.A=316 inches²**

3. A pyramid has a height of 14 inches, and bases are 10,12 inches. -what is the volume? V=1/3BH V=1/3(120)(14) V=1/3(1680)
 * V=560 inches³**

4. A pyramid's base is 5,7 inches, the slant height is 10 inches. -what is the surface area? S.A=1/2(L)(P)+B S.A=1/2(10)(24)+35 S.A=1/2(240)+35 S.A=120+35
 * S.A=155 inches²**

5. A cylinder has a radius of 2 and a height of 7. -what is the volume? V=(pi)R²H V=(pi)(4)(7)
 * V=87.92³**

6. A cylinder has a radius of 2 and a height of 7. -what is the surface area? S.A=2(pi)rh+2(pi)r² S.A=2(pi)(2)(7)+2(pi)2²
 * S.A=113.09²**

7. A cone has a base of 12(pi), height is 8 -what is the volume? V=1/3BH V=1/3(12(pi))(8)
 * V=32(pi)³**

8. A cone has a slant height of 6 and a radius of 10 -what is the surface area? S.A=(pi)(r)(l)+(pi)r² S.A=(pi)(10)(6)+(pi)10²
 * S.A=160(pi)²**

9. A sphere has a diameter of 10 -what is the volume? V=4/3(pi)r³ V=4/3(pi)5³
 * V=523.59³**

10. A sphere has a diameter 20 -what is the surface area? S.A=4(pi)r² S.A=4(pi)10²
 * S.A=700(pi)²**