Chapter 10

Sierra k

Chapter 10 Vocabulary words:

Vocab:

-Base of a parallelogram:the length of any one of its sides

-height of a parallelogram:the perpundicular distance between the base and the opposite side

-solid:three dimensional figure that encloses a part of space

-polyhedron:a solid that is enclosed by polygons

-sphere: a solid formed by all points in space that are the same distance from a fixed point

-cone:a solid with one circular base

-Surface area: the sum of the areas of its bases

-slant height:(l) of a regular pyramid is the height of a lateral face.

-Volume: a measure of the amount of space it occupies

-isometric drawing:another way to make a 2 dimensional drawing of a 3 dimensional figure

-net:a 2 dimensional pattern that forms a solid when it is folded

Formulas

Volume of a Cone: V=1/3*3.14*r2*h


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


Area of a parallelogram: A=b*h


Surface area of a Cone: S=3.14*r2+3.14*r*l


Volume of a pyramid: V=1/3*B*H


Volume of a prism: V=B*h


Surface Area of pyramid: S=B+1/2*P*l


Surface Area of a prism: S=2*B+P*h


Surface Area Of a cylinder: S=2*b+c*h=2*3.14*r2+2*3.14*r*h

Area of a Parallelogram

Examples+practice questions

Examples:

Area of a trapezoid


A=1/2(b1+b2)h

=1/2(12+18)(5)=75


Area of a circle


A=3.14*r^2

=3.14*3^2

=28.26


Surface area of a cylinder


S=2*3.14*r^2+2*3.14*h

=2*3.14*(9)^2+2*3.14(9)(26)

=1979.203


Surface area of a square pyramid


S=B+1/2PI

12^2+1/2(4*12)(9)

=360


Volume of a Prism


V=Bh

=1/2(7*14)(21)

=1029


Volume of a cone


V=1/3*3.14*r^2h

=1/3*3.14(7)^2(18)

=923.628

Practice question:

1)A movie theater serves a small size of popcorn in a conical container and a large sized popcorn in a cylindrical container. Find the volume of each container. Then determine which container is better to buy.


Volume of small container: Volume of larger container:

V=1/3*3.14*r^2h V=2.14*r^2h

=1/3(3.14)(3)^2(6) =(3.14)(2.5)^2(6)


=56.2in.^2 =117.75in^2