3herker

//this page is going to teach you how to find surface area and volume of shapes//

superb site for surface area and volume [|formulas] Understand ratios of surface area to volume Develop ideas of how to maximizing volume and minimizing surface area
 * 1) Section 1 **Surface area and Volume**
 * objectives**

surface area =** this is the total area of all the exposed sides of the object
 * //__Definition__//
 * volume** = number of overlapping units of cubes thats going to fill the object

//surface area and volume formulas// surface area = S volume = V length = L width = W height = H

for rectangle... S = 2LW + 2LH V = LWH

for cube... S = 6s² V = s³

2. section 2 **Surface area and volume of prisms**

Discover a formula for finding the surface area of an prism Discover a formula for finding the volume of an prism Use Cavalieri's Principle to discover a formula for a oblique or right prism
 * objectives**

__//surface area of a right prism formula//__ Surface area = S Lateral area = L Base area = B Perimeter = P Height = H

S = L + 2B or S = hp + 2B

//__volume of a prism__//

V = BH

altitude**- segment of a prism that has endpoints in the planes containing bases and is perpendicular to both planes
 * //__Definitions__//
 * height**- length of an altitude

3. section 3 **Surface area and volume of pyramids

objectives** Find a formula for the surface area of a regular pyramid Find a formula for the volume of a pyramid

//Pyramid// - a polyhedron consisting of base and three or more lateral faces. //Vertex of the pyramid// - lateral faces are triangles that share a single vertex //Base edge// - the lateral face that has one edge in common with the base //Altitude of a pyramid// - perpendicular segment coming from the vertex to the plane of the base //Height of a pyramid// - length of a pyramid's altitude //Regular pyramid// - a pyramid whose base is a regular polygon and whose lateral faces consist of congruent isosceles triangle //Slant height// - the length of an altitude of a lateral face of a pyramid
 * //definitions//**

surface area - S lateral area - L base area - B base perimeter - P slant height - L S = L + B or S = 1/2LP + B
 * Surface area of a Regular Pyramid**

4. section 4 **Surface area and volume of cylinders

objectives** Discover a formula for the surface area of a right cylinder Discover a formula for the volume of a cylinder

//Cylinder// - solid that is made of a circular region and its translated image on a parallel plane //Bases// - faces that are formed by it's circular region and translated image //Altitude of a cylinder// - a segment that has endpoints in the planes in the planes containing bases and it is also perpendicular to both planes //Height of the cylinder// - length of altitude //Axis of the cylinder// - segments joining the centers of two bases //Right cylinder// - a cylinder that is perpendicular to the bases //Oblique cylinder// - a cylinder that isn't perpendicular to the bases
 * Definitions**

S = L + 2B or S = 2πRH + 2πR²
 * surface area formula**

V = BH or V = πR²H
 * volume**

5. section 5 **Surface area and Volume of Cones

objectives** Discover a formula for the surface area of a cone Discover a formula for the volume of a cone

//cone// - three-dimensional figure that consists of a circular base and a curved lateral surface //lateral surface// - connects a base to a point //vertex// - point in the plane in a base //right cone// - altitude of cone intersects the base of the cone at the center //oblique cone// - altitude of cone that doesn't intersects the base of the cone at the center
 * Definitions**


 * Surface area of a cone**

Surface area - S Lateral area - L Base of area - B Radius - R Slant height - L

S = L + B or S=πRL + πR²


 * Volume of a cone**

Volume - V Radius - R Height - H Base area - B

V = 1/3BH or V = 1/3π²H

6. section 6 **Surface area and volume of Spheres

objectives** Discover and use a formula for the surface area of a sphere Discover and use a formula for the volume of a sphere

//sphere -// set of all points in a space that are the sane distance from a given point known as the center of sphere //annulus// - a ring-shaped figure
 * Definitions**


 * volume of a sphere**

Volume - V Radius - R

V = 4/3πR³


 * Surface area of a sphere**

Surface area = S Radius = R

S = 4πR²