QUESTION: What will change the surface area of a cylinder more, increasing the radius of the circle at the ends or increasing

Name: __________

Math 8

QUESTION: What will change the surface area of a cylinder more, increasing the radius of the circle at the ends or increasing the height of the cylinder?

Answer this question by investigating through Geometers Sketchpad. The following directions will guide you through building a cylinder:

1. CONSTRUCT THE 2 CIRCLE ENDS and CALCULATE AREA

a. Create a new sketch

b. Construct a circle using the circle tool

c. With the circle selected, measure the radius, circumference and area. Place the measures on or near the measured circle.

d. Construct a similar size circle a short distance below the first.

e. With the second circle selected, measure the radius only and dilate circle by selecting the center of the circle until the radius is equal to the first circle. (We can conclude that the both areas and circumferences will be equal.) We cannot copy circle since we will not be able to dilate it unless constructed.

2. CONSTRUCT CYLINDER LENGTH

a. Place a point on the side of the top circle and holding down the shift key place one on the same side of the bottom circle.

b. Under the CONSTRUCT menu select Segment

c. Measure line segment and place on segment

d. Repeat 2a, b and c on the opposite side of the circles creating the other side of the length of the cylinder.

3. CALCULATE AREA OF RECTANGULAR PIECE

a. Calculate the area of the rectangular part of the cylinder - circumference of the circle times the height of the cylinder.

4. CALCULATE THE TOTAL SURFACE AREA

a. Select calculate under measure

b. Add the area of the first circle, the area of the rectangular piece of the cylinder and the area of the second circle.

5. MAKE A TABLE TO SHOW RESULTS

a. Select together (using the SHIFT key) the radius of the circle (either one since they should be very close, the height of the cylinder, and the total surface area of the cylinder and under Measure select tabulate. A table is created.

If you haven’t saved your sketch do so at this point as we will begin to alter our measurements to analyze effect.

6. ALTER THE RADIUS OF THE CIRCLES

a. Select the center of the circle and increase the radius by .5

b. Do the same increase for the second circle

c. It may be necessary to select the line segment points on both sides of the bottom circle to insure the length of the cylinder remains the same.

d. Tabulate the new results of this new cylinder – highlight the radius, the length of the cylinder and the total surface area and select tabulate under measure. (Notice the calculations change as the figure is altered.)

e. To add to the current table, highlight the first entry and select Add Entry under Measure.

f. Save

g. Perform increase again and repeat 6 a thru e

7. ALTER THE LENGTH OF THE CYLINDER

a. Select the bottom circle

b. Holding down the shift key, hit the down arrow to increase the length until the length increases approximately .5 inches.

c. Create a new table. Highlight the same three measures that have been tabulated to now (the radius of the circle, the length of the cylinder and the total surface area) and select TABULATE under MEASURE.

d. Continue to increase the length by .5 inch and repeat steps 7a thru c. Remember to ADD ENTRY to the current table.

Analyze the two tables to answer the original query. Write your explanation for the results.