# Chapter 10

### Robert Prager

## Chapter 10 Formulas

Area of a Parallelogram: A = bh

Area of a Trapezoid: A = 1/2(b1 + b2)h

Area of a Circle: A = TTr^2

Surface Area of a Prism: S = 2B + Ph

Surface Area of a Cylinder: S = 2B + Ch = 2TTr^2 + 2TTrh

Surface Area of a Pyramid: S = B + 1/2Pl

Surface Area of a Cone: S = TTr^2 + TTrl

Surface Area of a Sphere: S = 4TTr^2

Volume of a Prism: V = Bh

Volume of a Cylinder: V = Bh = TTr^2h

Volume of a Pyramid: V = 1/3Bh

Volume of a Cone: V = 1/3Bh =1/3TTr^2h

Volume of a Sphere: V = 4/3TTr^3

## Section 1: Areas of Parallelograms & Trapezoids

Finding the area of a parallelogram is like that of a rectangle, as the same formula, A = bh, is used. An entirely different formula is used for finding the area of a trapezoid-A = 1/2(b1 + b2)h.

## Practice 1 Find the area of the parallelogram given that b = 3 & h = 8. | ## Practice 2 Find the area of the trapezoid given that b1 = 4, b2 =7, & h = 7. | ## Practice 3 Find the area of the trapezoid give that b1 = 10, b2 = 6, & h = 4. |

## Section 2: Areas of Circles

Circles have a formula unique to them for finding their areas-TTr^2. But there is an alternate option for finding the area of a circle. Divide a circle into at least 8 congruent sections, and arrange them so they somewhat resemble a parallelogram. Then find the area of the "parallelogram."

## Practice 1 Find the area of the circle given that r = 5. Use the formula TTr^2. | ## Practice 2 Draw a circle with a radius of 6 centimeters, divide it into 8 sections, & arrange them into a parallelogram to find the area. | ## Practice 3 Find the area given that r = 3. Try both formulas. (Draw a circle with a radius of 3 inches, and use the method of making it into a parallelogram). |

## Practice 2

Draw a circle with a radius of 6 centimeters, divide it into 8 sections, & arrange them into a parallelogram to find the area.

## Section 3: Three-Dimensional Figures

Solids are three-dimensional figures that take up part of a space. Some, called polyhedrons, are formed of polygons. The polygons are called faces. Cylinders, cones, & spheres are all examples of solids. Prisms & pyramids are examples of polyhedrons. Polyhedrons are classified by the shape of the base. Edges are where 2 faces meet. Vertices are where 2 or more edges meet.

## Practice 1 Classify the solid, & tell whether it is a polyhedron. Identify the number of faces, edges, & vertices. | ## Practice 2 Classify the solid, & tell whether it is a polyhedron. Identify the number of faces, edges, & vertices. | ## Practice 3 Classify the solid, & tell whether it is a polyhedron. Identify the number of faces, edges, & vertices. |

## Practice 1

## Practice 2

## Section 4: Surface Areas of Prisms & Cylinders

One way to find a polyhedron's surface area, or sum of the areas of its faces, is by using a net, a two-dimensional pattern that, when folded, creates a solid.

## Practice 1 Find the surface area of the prism given the dimensions shown. | ## Practice 2 Find the surface area of the cylinder given the dimensions shown. | ## Practice 3 Find the surface area of the cylinder (net) given that r = 8.5 & h = 9. |

## Section 5: Surface Areas of Pyramids & Cones

To the surface of a prism or cylinder, you must find the height. To find the surface area of a pyramid or cone, you need to find the slant height, which is the height along the slant.

## Practice 1 Find the surface area of the pyramid given the dimensions shown. | ## Practice 2 Find the surface area of the cone given that r = 5.2 & h = 8.7. | ## Practice 3 Find the surface area of the pyramid (net) given the dimensions shown. |

## Section 6: Volumes of Prisms & Cylinders

Volume is a measure of how much space an object takes up, and is measured in cubic units.

Note: Though cylinders & prisms use different formulas for finding their surfaces areas, finding their volumes uses the same formula: V = Bh.

## Practice 1 Find the volume of the prism given the dimensions shown. | ## Practice 2 Find the volume of the cylinder given the dimensions shown. | ## Practice 3 Find the volume of the cylinder given the dimensions shown. |

## Section 7: Volumes of Pyramids & Cones

Finding the volume of a pyramid or cone is similar to that of a prism or cylinder. The difference is a pyramid has 1/3 the volume as a prism with the same base area & height-same goes for cylinders & cones.

## Practice 1 Find the volume of the pyramid given the dimensions shown. | ## Practice 2 Find the volume of the cone given the dimensions shown. | ## Practice 3 Find the volume of the cone given the dimensions shown. |