SLICING UP A VOLCANO

NAME:CLASS:DATE:

PART A – AREA AND VOLUME FORMULAS

A1 Go to https://www.mathsisfun.com/area.html and review.

Define area in your own words?>

Are there any area formulas you didn’t know? If so, which ones?>

What is the area for a circle?>

What is a mnemonic?>Website URL: What is a mnemonic for the area of a circle?>

Define pi in your own words?>

What are the first 15 digits of pi?>

In Excel, how do you “call up” pi to use in a calculation?>

What are two common approximations for pi? One being a decimal and one being a fraction.>

A2 Go to https://www.khanacademy.org/math/basic-geo/basic-geo-volume-sa/volume-cones/a/volume-formulas-review and review.

Define volume in your own words?>

Are there any volume formulas you didn’t know? If so, which ones?>

What is the volume for a cylinder?>

What is the volume for a cone?>

What is a prism?>Website URL:

True or False. For all prisms you can find the volume by the formula V=A*h where A is the area on an end and h is the height.>

What is a pyramid?>Website URL:

Compare the formulas for a cone and cylinder. Then compare the formulas for a pyramid and rectangular prism. What do you notice?>

True or False. For all pyramids you can find the volume by the formula V=1/3*A*h where A is the area of the base and h is the height.>

PART B – VOLCANOES

B1 Search the web using the key words “most perfect volcano images”. Try to find 3 that resemble perfect cones. Copy and paste images along with the name of the volcano in the table below. Resize appropriately.

Volcano 1 Volcano 2 Volcano 3Image 1 Image 2 Image 3

B2 Try to find the height and diameter (or radius) of 1 of the 3 volcanoes above. If you can’t find the information for those volcanoes, find another volcano for which you can. Name:Height:Diameter:Website URL:

B3 Find the volume of the volcano above using the formula you found earlier in A2. Make sure to include units.>

PART C – SIMILAR TRIANGLES

C1 Search the web for “similar triangles”. What does it mean when they say the sides of similar triangles are proportional? You can use either of the images above to help you answer the question.>Website URL:

C2 Assume we represent a volcano as a cone pointed up with height H and diameter D. Bisect the cone vertically such that the bisector is H. About halfway up (let this distance be x), draw a horizontal line from the bisector to the edge of the cone (label this distance r). We are interested in finding the length of r depending on x – in other words, we want to find r(x) for our cone with height H and diameter D. Draw and label a good picture below.>

C3 Fill in the blank and set up the proportion r is to D/2 as H-x is to ___.>

PART D – Excel

D1 Open the Slicing Up A Volcano Excel file. Assume our volcano is a perfect cone with a height of 1000 feet and a diameter of 1000 feet. Enter 1000 for H and 1000 for D on the Excel sheet named Cone. Compete the table based on the Output of Excel.

xheightin feet

rradiusin feet

aarea at r

in square feet

vvolume of slice

in cubic feet0

2505007501000

D2 What is the volume of the volcano using the formula? (cell B7)>What is the approximate volume of the volcano adding up the 5 slices? (cell E20)>What is the thickness of the slices we are adding up?>What is the shape of the slices we are adding up?>Explain why the approximation of the volume is an overestimation?>

D3 What is Excel doing?

Click on B7 and look at text box. What is the Excel formula and what is it trying to calculate? >

Click on D7 and look at text box. What is the Excel formula and what is it trying to calculate? >

Click on B10 and look at text box. What is the Excel formula and what is it trying to calculate? >

Click on D16 and look at text box. What is the Excel formula and what is it trying to calculate? >

Click on E16 and look at text box. What is the Excel formula and what is it trying to calculate? >

Click on E20 and look at text box. What is the Excel formula and what is it trying to calculate? >

D4 Let’s calculate the volume of the volcano you found in B2 above. Go to the second sheet of Excel called My Volcano. Enter in the height and diameter for your volcano. Save the Excel file.

What is the volume of the volcano using the formula? (cell B7)>What is the approximate volume of the volcano adding up the 100 slices? (cell E112)>What is the thickness of the slices we are adding up?>How could we get a better approximation?>

D5 Save this Word document and the Excel file with the information for your volcano in D4 then submit via Canvas.

My favorite volcanoExtra credit for knowing the name of the volcano and the lake