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**1-7 Three Dimensional Figures**

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

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

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**They can be classified as prisms or pyramids.**

A prism has two congruent faces called bases connected by Parallelogram faces. A pyramid has a polygonal base and three or more triangular faces that meet at a common vertex.

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

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**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.

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**Identify each solid and their base(s)**

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

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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(top & bottom) + 2(front & back) + 2(left & right) T = 2(lw) + 2(lw) + 2(lw) T = 2(5)(2) +2(5)(6) + 2(2)(6) T = 20 in in in2 T = 104 in2

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**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 What shape is the base? square (s2) T = 4(½bh) + s2 T = 4(½)(24)(13) + 242 T = 624 cm2 + 576 cm2 T = 1200 cm2

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**Cylinder – a parallelogram and two circles.**

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). T = Hpd + 2pr2 T = 6(p4) + 2p22 T = 75.4 ft ft2 T = ft2

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

Volume of a prism is the height (h) of the prism times the area of the base (B) : 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) : What shape is the base? square (s2) V = ⅓Hs2 V = ⅓(5)(242) V = ⅓(5cm)(576 cm2) V = ⅓(5cm)(576 cm2) V = 960 cm3

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

V = Hpr2 V = 6 ft(p)(2 ft)2 V = 24p ft3 V = 75.4 ft3

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