3keldre

This page will teach you about Surface Area and Volume.
[|cones] -We are going to look into the concepts of maximizing volume and shrinking surface area.

Surface Area and Volume Formulas: S=2lw+2wh+2lh and V=lwh =BOX

S=6s² and V=s³ =CUBE

Example: If the box above was 6x4x2, with the length being 6, the height being 4, and the width being 2, what would the surface area be? 2x6x2+2x2x4+2x6x4= Surface area of the box above.

SECTION 2:

-Use a formula to find the surface area of a right prism. -Use a formula to find the volume of a right prism. -Use Cavalieri's Principle to develop a formula for the volume of a right prism or an oblique prism.

Altitude: a segment that has endpoints in the planes containing the bases and that is perpendicular to both planes. Height: the length of an altitude. Surface Area of a Right Prism: Surface Area, S, of a right prism with lateral area L, base area B, perimiter p, and height h is: S=L+2B or S=hp+2B.

Volumes of Right Prisms: The formula would be V=lwh with l=length and w=width and V= volume. Sometimes you can also use this formula for finding the volume of a Right Prism it depends on the base. V=Bh. B=base.

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

Volume of a Prism: The volume which is V, of a prism with the height being h and base area B is V=Bh.

Section 3:

- Define and use a formula for the surface area of a regular pyramid. - Define and use a formula to find the volume of a pyramid. Pyramid- is a polyhedron consisting a base Base- a polygon, and three or more lateral faces Lateral faces- are triangles that share a single vertex Vertex of a pyramid- to share a single vertex Base edge- has one edge in common with the base Lateral edge- the intersection of two lateral faces Altitude- is the perpendicular segment from the vertex to the plane of the base Height- is the length of its altitude Regular pyramid- is a pyramid whose base is a regular polygon and whose faces are congruent isosceles triangles Slant height- the length of an altitude of a lateral face of a regular 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 l is S=L+B or S= 1/2lp+B

Volume of a Pyramid- The volume, V, of a pyramid with the height h and the base area B is V=1/3Bh

Section 4:

- Define and use a formula for the surface area of a right cylinder. - Define and use a formula for finding the volume of a cylinder. -CYLINDERS:

Cylinder- is a solid that consists of a circular region and its translated image on a parallel plane Lateral surface- connects the circles of the plane Bases- the faces formed by the circular region and its translated image Altitude- is a segment that has endpoints in the planes containing the bases and is perpendicular to both planes Height- is the length of an altitude Axis- is the segment joining the centers of the two bases Right cylinder- the axis of a cylinder os perpendicular to the bases Oblique Cylinder- the axis is not perpendicular to the bases

-Surface Area of a Right Cylinder: The surface area, S, of a right cylinder with lateral area L, base area B, radius r, and the height h is S=L+2B or S=+ 2πrh+2πr².

-Volume of a Cylinder: The volume, V, of a cylinder with the radius r, height h, and base area B is V=Bh or V=πr²h.

Section 5:

- Define and use the formula for the surface area of a cone. - Define and use the formula for the volume of a cone.

CONES:

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, called the vertex.

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

If the altitude of a cone intersects the base of the cone at its center, the cone is a right cone. If not, it is an oblique cone.