dinmic

dimi309 Chapter 9 link
= = =**Chapter 7**=

7.1 Surface Area and Volume
 * The surface area of an object is the total area of all the exposed surfaces of the object. Example: The skin of a banana.
 * The volume of a solid object is the number of nonoverlapping unit cubes that will exactly fill the interior of the figure. Example: Water in a glass.
 * Surface area and volume equation of a rectangular prism:
 * Surface area: S=2lw+2wh+2lh
 * Volume: V=lwh

Two solar panels have the same voume, but different dimensions. Panel 1: 3*5*3 Panel 2: 1*5*9 Which solar panel has more surface area, thus making it the better panel? [|Surface Area Explanation] [|Volume puzzle]

7.2 Surface Area and Volume of Prisms
Altitiude of a prism: Segment that has endpoints in the planes containing the bases and that is perpendicular to both planes Example: unsharpened pencil Height: Length of the altitude Surface Area of a Right Prism: S= L + 2B or S= hp + 2B where h= Height p= Perimeter B= Base L=hp



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 volumes.

It means that a prism at a slant and a straight prism that are the same height are equal if the middle areas of each prism are parallel to the bases of each prism.

Volume of a prism: V=Bh Volume equals base times height.

A company has designed a right rectangular prism box for their product. It has the dimensions of 4*6*3 Find the volume.

7.3 Surface Area and Volume of Pyramids
Pyramid: Polyhedron consisting of a base, which is a polygon, and three or more lateral faces. Example: pyramids in Egypt

Base: The faces formed by the polygonal region and its image. The bottom of the pyramid.

Lateral face: The faces of a prism or pyramid that are not bases. The sides of the pyramid.

Vertex of the pyramid: The lateral faces are triangles that share a single vertex. The tip of the pyramid.

Base edge: Each lateral face has one edge in common with the base. Where the lateral face and base meet.

Lateral Edge: Intersection of two lateral faces.

Altitude: Perpendicular segment from the vertex to the plane of the base.

Height: length of a pyramid's altitude.

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

Slant height: The length of an altitude of a lateral face of a regular pyramid. Length of the side.

Surface area of a regular pyramid: S=L+B or S=1/2xp+B L= lateral area B= Base area p= Perimeter of base x= Slant height

This equation wants you to take the slant height and multiply it by the perimeter of the base and then multiply it by 1/2. Then take that number and add it to the area of the base to find the surface area.

Volume of a Pyramid: V=1/3Bh B= base area h= height

This equation wants you to multiply the base area by the height of a pyramid and then multiply that by 1/3.

Jimmy's miniature square pyramid has a base edge of 4 meters, a height of 6 meters, sarah's square pyramid has a base edge of 5 meters and a height of 8. Which pyramid has more volume?

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. Example: a straw Lateral surface: Connects the circles of a cylinder.

Bases: The faces formed by the circular region and its translated image are called the bases of the cylinder.

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

Height: The length of an altitude.

Axis: Segment joining the centers of the two bases.

Right cylinder: The axis is not the perpendicular to the base.

Surface area of a right cylinder: S=L+2B or S=2(Pi)rh+2(Pi)r^2

(Pi)= 3.14

r= radius

h= height

This equation requires you to multiply Pi by radius and height. Then add that number to Pi multiplied by radius to the second power.

Volume of a cylinder: V=Bh or V=(Pi)r^2h

(Pi)= 3.14

r= radius

h= height

This equation wants you to multiply (Pi) by radius to the 2 power and height.

[|Extra Cylinder Help]

A soup company sells its soup in cans with a diameter of 6 inches and a height of 8 inches. find the surface area.

7.5 Surface Area and Volume of Cones
Cone: A 3-D 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 called the vertex. Example: traffic cones Base: circular base

Lateral surface: Curved lateral surface

Altitude: The perpendicular segmentfrom the vertex to the plane of the base.

Height: The length of the altitude.

Right cone: If the altitude intersects the center of the cone.

Oblique cone: If the altitude does not intersect the center of the cone.

Surface area of a right cone: S=L+B or S=(Pi)rx+(Pi)r^2

(Pi)= 3.14

r= radius

x= slant height

This equation wants you to multiply Pi by radius and the slant height and add Pi multiplied by the radius to the 2 power.

Volume of a cone: V=1/3Bh or V=1/3(Pi)r^2h

This equation wants you to multiply Pi by radius to the 2 power and height. Then multiply by 1/3

[|Cone help from Dr. Math]

Ben's Ice cream cone has a radius or 2 and a slant height of 5, while Harry has an ice cream cone with a radius of 3 and a slant height of 4 Which cone holds more ice cream?

7.6 Surface Area and Volume of Spheres
Sphere: A set of all points in space that are the same distance, r, from a given point known as the center of the sphere. Example: a ball



Annulus: Ring shaped figure in the cylinder. If you cut the cylinder in half you would see this.

Volume of a sphere: V=4/3(Pi)r^3

(Pi)= 3.14

r= radius

This equation wants you to take Pi and multiply it by radius to the 3 power.Then multiply it by 4/3.

Surface area of a sphere: S=4(Pi)r^2

To find the surface area you should take Pi and multiply it by radius to the 2 power and then take that number and multiply it by 4.

A beach ball has a diameter of 10. find the radius and the surface area.

[|Surface Area of a Sphere]

Answers 7.1: Panel 2

7.2: 72 units cubed

7.3: sarah's pyramid

7.4: 207.24 inches squared

7.5: Harry's ice cream cone holds more

7.6: Volume: 314 units cubed Surface area: 523.32 units squared

1. A triangular prism has a height of 4 feet and the base has sides of 10, 24, 26. Find the volume: V=Bh V=(120)(4) V=480 feet cubed

2. A triangular prism has a height of 6 feet and base sides of 6, 4, 9. Find the surface area: S=hp+2B S=(6)(19)+2(12) S=114+24 S=138 feet squared

3. A pyramid has a height of 12 feet and base dimensions of 4 X 5 feet. find the volume V=1/3Bh V=1/3(20)(12) V=1/3(240) V=80 feet cubed 4. A pyramid has a base dimension of 6 X 7 feet and has a slant height of 8 feet. Find the surface area: S=1/2(l)(p)+B S=1/2(8)(26)+(42) S=1/2(208)+(42) S=104+42 S=146 feet cubed

5. A can of soup has a radius of 3 inches and a height of 7 inches. Find the volume: V=(Pi)r^2h V=(Pi)3^2(7) V=(Pi)9(7) V=(Pi)63 V=197.82 inches cubed

6. Another can of soup has a radius of 4 inches and a height of 8 inches. Find the surface area: S=2(Pi)rh+2(Pi)r^2 S=2(Pi)(4)(8)+2(Pi)4^2 S=2(Pi)(32)+2(Pi)(16) S=(Pi)(64)+2(50.24) S=200.96+100.48 S=301.44 inches squared

7. An ice cream cone has a diameter of 4 inches and a height of 7. Find the volume: V=1/3(Pi)(r^2)(h) V=1/3(Pi)(2^2)(7) V=!/3(Pi)(4)(7) V=1/3(Pi)(28) V=1/3(87.92) V=29.27 inches squared

8. Another ice cream cone has a slant height of 5 and a radius of 4. Find the surface area: S=(Pi)rl+(Pi)r^2 S=(Pi)(4)(5)+(Pi)(4^2) S=(Pi)(20)+(Pi)(16) S=62.8+50.24 S=113.04 inches squared

9. A sphere has a radius of 5 feet. Find the volume V=4/3(Pi)(r^2) V=4/3(Pi)(5^2) V=4/3(Pi)(25) V=4/3(78.5) V=104.64 feet cubed

10. A ball has a radius or 4 feet. Find the surface area: S=4(Pi)(r^2) S=4(Pi)(4^2) S=4(Pi)(16) S=(64)(Pi) S=200.96 feet squared