Melissa's geometry blog: April 2012

Sunday, April 22, 2012

April 17,2012

Aim: How do we find the volumes of pyramids and cones?

Volume formula for the pyramid and cone :

V: 1Bh
       3

For the volume for pyramid and the cone you have to divide by three.

      In the formula for the pyramid the B stands for the area of the base.

In this case the base is a square so to find the area of the base we would use the length of the square and multiply it by its self so : length of one side ^{2 .}
^{After that multiply it by the height and divide it by three.}

^Cone:
^{The cone can have the same formula as the pyramid but it can also be shown this way :}
V: 1πr2H

3

πr2 is used instead of the area of the base which is a circle.

^{try it :}

	Choose: 2,095,533 20,955,334 43,442,812 74,350,037
The Pyramid of Khafre was built for the son of Khufa, for whom the Great Pyramid was built. It is slightly smaller in size than the Great Pyramid. The height is 447.5 feet. The base side length is 706 feet. Find the volume of the Pyramid of Khafre to the nearest cubic foot.

^{images: http://regentsprep.org/Regents/math/geometry/GG2/PyramidPage.htm}
^{http://regentsprep.org/Regents/math/geometry/GG2/ConePage.htm}
Try it : http://regentsprep.org/Regents/math/geometry/GG2/PracSol.htm

April 18,2012

Aim: How do you find the surface area and volume of a sphere?

fist of all :)
what are spheres?
A sphere is a figure that holds all set of points in space that are equidistant from a given point

To find the volume of the sphere you need to use the formula :
            V= 4πr3
            3
for example:
in a sphere we have a radius of 4,find the volume and leave it to the nearest tenth

First we plug in things we know :
V= 4π43
            3
Next:
we solve the exponent and multiply the number :
V= 4π64 = 256π
          3           3
Then :
tell divide the number and leave π there
the final answer is :

v = 85.33π

to find the Surface area the formula is :

SA: 4πr2

Ex: a sphere has a radius of 4find the surface area:

First plug in everything you know:

SA: 4 π42

Next:solve what the exponents and also multiply by 4

4* π*16= 64*π

Finally :

your answer can be left as terms of π or to the nearest tenth.

64π or 201.1

TRY IT :D

1.		Soda is sold in aluminum cans that measure 6 inches in height and 2 inches in diameter. How many cubic inches of soda are contained in a full can? (Round answer to the nearest tenth of a cubic inch.)	Choose: 12.0 18.8 24.0 75.4

sources used:

regents prep:

http://regentsprep.org/Regents/math/geometry/GG2/PracSol.htm

Google images:http://knowledgepublications.com/doe/images/DOE_Mathematics_Sphere.gif

Sunday, April 1, 2012

March 28,2012

Aim:How do we find the surface area and lateral area of a cylinder?

To find the surface area of a cylinder we first need a formula.

when having the formula we then apply it to the cylinder.
A cylinder has two bases that are circles.
if we didnt know the equation we could solve the area for the circle and multiply it by 2 since there is two circles.

After we have the area of the circle we then have to find the area of the other part of the cylinder which is called the lateral area. The lateral area and the area of the two bases are the total surface area.

For example:

2= raduis
6= height

To find the total surface area we need the formula.
SA= 2πrh+2πr ²

PLUG IN:
SA= 2*π*2*6+ 2*π*(2) ²

Solve parts of the equations.( leave in terms of π if told so)
SA= 2πrh
2* π*2*6
2*2*6= 24
add the π

First part of the equation would be: 24π

Second part of the equation:
SA= 2πr ²
2*π*(2)2
(2)2 =4
so 4*2= 8
plus π
answer to the second half: 8π

ADD them together and the answer would be 30 π

NOW YOU TRY:D

A cylinder has a height of 8 and a radius of 4
find the surface area.
leave in terms of π.

SOURCES USED:
http://www.mathwarehouse.com/solid-geometry/cylinder/images/cylinder-area-problem1.jpg
http://www.regentsprep.org/regents/math/algebra/AS2/Solids.htm