morben

//**__7.1 Surface Area and Volume__**// Objectives- Explore ratios of surface area to volume. Objectives- Develope the concepts of maximizing volume and minimizing surface area. S=2L+2wh+2Lh V=Lwh Surface area and volume of a cube. S=6s2 v=S3
 * Surface area and volume of a right rectangular prisim.

Activity 1

Length Surface Area volume Ratio**
 * **1** || **6** || **1** || **6/1** ||
 * **2** || **7** || **2** || **7/2** ||
 * **3** || **11** || **3** || **11/3** ||
 * **n** || **6** || **1** || **6/1** ||


 * **side,s** || **surface area** || **volume** || **Ratio** ||
 * **1** || **6** || **1** || **6/1** ||
 * **2** || **7** || **2** || **7/2** ||
 * **3** || **11** || **3** || **11/3** ||
 * **n** || **6** || **1** || **6/1** ||


 * //__7.2 Surface Area and volumes of Prisims.__//**

Objective-Define and use a formula for finding the volume of a right prism. Objective-Define and use a formula for finding the surface ara of a right prism. Objective-Use cavalieris principle to develop a formula for the volume of a right or oblique prism. The surface area of a prism maybe broken down into two parts: the base area and lateral area S= L+2B or S=hp+2B** Example 1 The area of the base is. **B** =1/2(2)(21)=
 * Altitude- Segment that has endpoints in the planes containing the bases and is perpendicular to both planes.**
 * Height- The length of an altitude.**
 * Surface area of a right prism.
 * 21

The perimeter of each base. P=10+21+17=48 so the lateral area is. L=hp=30(48)=1440. and the surface area is. s=L+2B=1440+2(21)=1440+42=1482

Example 2** An aquiarium in the shape of a right retangular prismhas the dementions of 110x50x7 feet. Given that approx. 1 gallon =0.134 cubic feet, how many gallons of water will the aquarium hold? Given 1 gallon of water= 8.33 pounds, how much will he water weigh? V=(110)(50)(7)=38,500 cubic feet V=38,500 divided by .134=287,313 gallon weight= 287,313(8.33)=2,393.317 pounds

An aquarium has the shape of a right regular hexagonal prism with the demensions 14in, 48in, and 7 square root of 3. The base of the aquarium has a perimiter of (14)(6), or 84in and apothem of 7 square root of 3 in, so the base area is found as follows: B=1/2ap=1/2(84)(7 square root of 3)=294 square root of 3= 509.22 square inches The volume is V=Bh=(294 square root of 3)(48)=14112 square root of 3= 24,443 cubic inches
 * Example 3**
 * Solution**

If two solids have equal heights and the cross sections form by every plain parallel to the bases of both solids have equal areas, then the two solids have equal volumes.
 * Cavalieri's Principle**

A pyramid is a polyhedron consisting of a base, which is a polygon and three or more laderal faces, the laderal faces are triangles that share a single vertex, called the vertex of a pyramid. Each lateral face has one edge is common with the base, called a base edge. The intersection of two lateral faces is a lateral edge. The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base. The height of a pyramid is the lengh of its altitude. A regular pyramid is a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles. In a regular pyramid, all of the lateral edges are congruent, and the altitude intersects the base at its center. The lengh of an altitude of a lateral face of a regular pyramid is called the slant height of the pyramid
 * //__7.3 surface area and volume of pyramids__//**

The surface area is the sum of the lateral areas and the base area S=L+B S=4(1/2sl)+s squared OR S=1/2l(4s)+s squared 4s is the perimeter of the base. S=1/2lp+s squared
 * Example 1**

The area of the roof is the lateral ares of the pyramid. L=1/2lp=1/2(6)(8X4)=96 sqaure feet The volume of a pyramid is found as follows. V=1/3Bh =1/3 (776squared)(481) =96,548,885 cubic feet The weight in pounds is 96,548,885 cubic feet X 167 pounds per cubic foot = 16,123,663,850 pounds, or 8,061,831 tons.
 * Example 2**
 * Example 3**

A cylinder is a solid that consists of a circular regein and its translated image on a parallel plane, with a lateral surface connecting the circles. The faces formed by the circular regien and its translated image are called the bases of the cilinder. An altitude of a cylinder is a segment that has end points in the planes containing the bases and is perpendicular to both planes. The height of a cylinder is the lengh of an altitude. The axis of a cylinder is the segment joining the centers of the two bases. The radius of a penny is half of the diameter, of 19.05 millimeters. Use the formula for the surface area of a right cylinder. S=3.14rh+2(3.14) S= 2(3.14)(9.525)(1.55)+2(3.14)(9.525)squared=663.46 square millimeters
 * //__7.4 Surface area and volume of cylinders__//**
 * Example 1**