1-7 Three Dimensional Figures

Objectives:The student will be able to:1. Identify and name three-dimensional figures.2. Find surface area and volume.

Polyhedron – a solid with all flat surfaces that enclose a single region of space.

Solids

A few things to know about Polyhedrons:

1. Each flat surface, or face, is a polygon.

2. The line segments where the faces intersect are called edges.

3. The point where three or more edges meet is called a vertex.

4. They can be classified as prisms or pyramids.

A. A prism has two congruent faces called bases connected by Parallelogram faces.

B. A pyramid has a polygonal base and three or more triangular faces that meet at a common vertex.

5. They are named by the shape of their bases.

Cylinder – parallel circular bases connected by a curved surface.

Cone – a circular base connected by a curved surface to a single vertex.

Sphere – a set of points in a space that are the same distance from a given point.

Identify each solid and their base(s). If it is a polyhedron, name the faces, edges, and vertices.

Triangular Prism Cylinder Square pyramid

Surface Area

Surface area – the sum of the areas of each face of a solid.

A rectangular prism is made up of 6 rectangular (A = lw) faces. The total surface area (T) is the sum of the area of each face:

T = 2(lw) + 2(lw) + 2(lw)

T = 2(top & bottom) + 2(front & back) + 2(left & right)

T = 2(5)(2)+2(5)(6) + 2(2)(6)

T = 20 in2 + 60 in2 + 24 in2

T = 104 in2

A pyramid is made up triangles (A = ½bh) and a base (Area of a base).

The total surface area (T) is the sum of the area of each face plus the Area of the base.

How many sides are there? 4

T = 4(½bh) + s2

What shape is the base? square (s2)

T = 4(½)(24)(13) + 242

T = 624 cm2 + 576 cm2

T = 1200 cm2

Cylinder – a parallelogram and two circles.

T = Hpd + 2pr2

T = 6(p4) + 2p22

T = 75.4 ft2 + 25.1 ft2

T = 100.5 ft2

The total surface area (T) is the height (H) of the cylinder times the circumference (pd) of the cylinder plus two times the area of the base (pr2).

Volume of a prism is the height (h) of the prism times the area of the base (B) :

Volume

V = hB

V = 6(2)(5)V = 60 in3

Volume of a pyramid is ⅓ the height (H) of the pyramid times the area of the base (B) :

V = ⅓Hs2

What shape is the base? square (s2)

V = ⅓(5)(242)

V = ⅓(5cm)(576 cm2)V = ⅓(5cm)(576 cm2)V = 960 cm3

Volume - the measure of the amount of space the solid encloses.

Volume (V) of a cylinder is the Height (H) times the Area of the base (A = pr2).

V = Hpr2

V = 6 ft( )(2 p ft)2

V = 24 p ft3

V = 75.4 ft3