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.

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."

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.

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.

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.

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.

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.