YEAR 10 CAS PROJECT – ARTIFICIAL TREES
1. Identify a label in the diagram of the tree that is ambiguous.
2. Convert all dimensions to centimetres. You will need to find how to convert
from feet and inches to centimetres. See calculator hints below.
3. Make a new table, which will show all dimensions in centimetres. Store the
computed values on your calculator.
4. Write down the formula for the surface area of any cone in terms of its radius
and slant height. Define it as ‘sa’ on your calculator. Hint: the formula for the
side surface are of the cone is given by: SA = π × r × s , where r is the radius of
the base and s is the slant height. Please refer to the diagram above.
5. Use the formula to compute the surface area of each of the three trees,
excluding tree stems. Assume that the shortest tree has a stem height of 6
inches and the two taller trees have stem heights of 12 inches. All calculations
and results need to be in cm and cm2. You will need to calculate slant height
for each tree. Again store your results as h1 , h2 , h3 (Numbers only, without
units) and similarly s1 , s2 , s3 and r1 , r2 , r3 . You will notice that r1 , r2 , r3 are
reserved variables so let call the radii as l1 , l2 , l3 . Use your define ‘sa’ function
and lists to calculate three surface areas in one computation on a calculator.
©Bozenna Graham 2008
Wesley College
Melbourne, Australia
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Write down your results in a table. You may store those as a1 , a2 , a3 for further
calculations.
6. Convert each surface area to m2 using the conversion 1 m 2 = 10000 cm 2 .
7. For each tree, calculate the following:
a) Concentration of lights per square metre of surface area.
b) Concentration of tips per square metre of surface area.
c) Percent of tips that are lighted, assuming that all lights are at the tips of
the branches.
8. Tabulate your results for Question 7.
9. Choose the ‘best lit’ tree from your point of view and justify your choice.
Calculator Hints:
• For unit conversions: select Units, Length,_ft or _in. Check that your
calculator is set up in SI units.
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• To convert from feet to metres: 2_ft Enter
• Then multiply by 100 to convert metres to centimetres by pasting the
answer in metres, delete the units and times 100.
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To convert from inches to centimetres:
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Define the surface area as:
©Bozenna Graham 2008
Wesley College
Melbourne, Australia
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Calculate the surface area for
each tree using lists:
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