Chapter 10

Derek Brown

Section 1

Base of parallelogram: the length of any one of its sides.

Height of parallelogram: the perpendicular distance between base and opposite side.

Base of trapezoid: its two parallel sides.

Height of trapezoid: perpendicular distance between the bases


PRACTICE QUESTIONS AND EXAMPLES

A=1/2(b1+b2)h

=1/2(6+13)3

=33in ^2


A=1/2(b1+b2)h

=1/2(2*6+2*16)(2*3)

=132in ^2

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Section 2

Areas of Circles

A=pi*r^2

Use the pi button to get exact answers or if test says so, use 3.14

Radius: the measurement from center of circle outward

Diameter: distance from one side of circle to another, passing through the center

Circumference: the distance around the circle. (like perimeter)


PRACTICE QUESTIONS AND EXAMPLES

A=pi*r ^2


=3.14(5)^2

=78.5 in.^2


530.66=(3.14)r^2

169=r^2

169/169=r

13=r

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Section 3

Solid: A three dimensional figure that encloses a part of space.

Polyhedron: A solid that enclosed by polygons.

Prism: a polyhedron with two congruent bases.

Pyramid: a polyhedron that has one base and other faces are triangles.

Cylinder: Solid with two congruent circular bases.

Cone: A solid with one circular base.

Sphere: All points in space that are the same distance from a point in the center.

Edges: Segments where faces meet.

Vertex: a point where 3 or more edges meet.


PRACTICE QUESTIONS AND EXAMPLES


You want to find out the size of your basketball to know if its a small ball or a large ball, it doesn't tell you on the ball so you have to figure out the size yourself. You can measure the circumference and figure out the size of the sphere.

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Section 4

Net: A two dimensional pattern that forms when a solid is folded.

Surface Area: The sum of the areas of its faces.


PRACTICE QUESTIONS AND EXAMPLES


S=2pi*r^2+2pi*r*h


=2pi(4)^2+2pi(4)(10.7)

=369.45

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Section 5

Slant Height: the height of a lateral face, that is not the base.

You need this to find the area of a cone and a pyramid.


PRACTICE QUESTIONS AND EXAMPLES


Finding the perimeter or a rectangular pyramid:

Find the perimeter of the base,

Substitute into the formula for surface area

Solve the rest of the problem.

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Section 6

Volume: measure of the amount of space an object occupies.

Bind the volume with the formula: V=B*h


PRACTICE QUESTIONS AND EXAMPLES

v=Bh

=pi*r^2h

=pi(3)^2(9)

=81*pi

=254.469

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Section 7

Pyramid: a polyhedron that has one base and other faces are triangles.

Cone: A solid with one circular base.

Volume: the amount of space an object takes up.


PRACTICE QUESTIONS AND EXAMPLES

v=1/3BH

=1/3(1/2*24*10)(12)

=480

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FORMULAS

Area of parallelogram: a=b*h

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

Area of Circle: A=pi*r^2

Circumference of Circle: C=r*pi*2

Volume of prisms: V=B*h (B=b*h)

Volume of pyramid: V=I*w*h/3

Volume of Cylinder: B*h (B=b*h)

Volume of cone: V=pi*r^2*h/3

Lateral Surface area of Cone: A=pi*r*l

Volume of sphere: V=4/3*pi*r^3

Surface area of sphere: the area of the circle with same diameter*4

Volume of a Cone
Volume of a Prism - MathHelp.com - Math Help
Surface Area Of A Sphere - VividMaths.com