Procedure Part A: Circles and Ratio of Circumference/Diameter 1. Obtain three different sizes of cups, containers, or beakers with circular cross section. Trace around the bottoms to make three large but different-sized circles on a blank sheet of paper. 2. Mark the diameter on each circle by drawing a straight line across the center. Measure each diameter in cm and record the measurements in Table 2.1. Repeat this procedure for each circle for three times. 3. Measure the circumference of each circle by carefully positioning a string around the object’s base, then mark the place where the string ends meet. Measure the length in cm and record the measurements for each circle in Table 2.1. Repeat the procedure for each circle for three trials. Find the ratio of the circumference of each circle to its diameter. Fill the ratio for each trial in Table 2.1. 4. The ratio of the circumference of a circle to its diameter is known as pi (symbol π), which has a value of about 3.14. Compare your ratio with 3.14. Are they close? TABLE 2.1 Circles and Ratios Small Circle Medium Circle Large Circle Trial 1 2 3 1 2 3 1 2 3 Diameter (D) 5.5 5.4 5.5 8.7 8.5 8.6 12.5 12.4 12.3 Circumference (C) 18.0 18.3 17.8 24.7 27.1 27.6 38.9 38.6 38.7 Ratio of C/D Average C/D = _________________________________ Part B: Area and Volume Ratios 1. You will be given three cubes with different size. Note that a cube has six sides, or six units of surface area. The side of a cube is also called a face, so each cube has six identical faces with the same area. The overall surface area of a cube can be found by measuring the length and width of one face (which should have the same value) and then multiplying (length)X(width)X(number of faces). Use a metric ruler to measure the cube, then calculate the overall surface area and record your finding for this each cube in Table 2.2. 2. The volume of a cube can be found by multiplying the (length)(width)(height). Measure and calculate the volume of the cube and record your finding for each cube in Table 2.2. 3. Calculate the ratio of surface area to volume for each cube and record it in Table 2.2. 4. You only need calculate the surface area, the volume, and the ratio of surface area to the volume of each cube. 5. Is there a trend or a pattern, or generalization, concerning the volume of a cube and its surface area to volume ratio. For example, as the volume of a cube increases, what happens to the surface area to volume ratio? TABLE 2.2 Area and Volume Ratios Small Cube Medium Cube Large Cube Length of side (cm) 2 cm 4 cm 6 cm Surface Area, cm2 Volume (cm3) Ratio of Area/Volume ________(cm2)/(cm3) _______
Procedure
Part A: Circles and Ratio of Circumference/Diameter
1. Obtain three different sizes of cups, containers, or beakers with circular cross section. Trace around the bottoms to make three large but different-sized circles on a blank sheet of paper.
2. Mark the diameter on each circle by drawing a straight line across the center. Measure each diameter in cm and record the measurements in Table 2.1. Repeat this procedure for each circle
for three times.
3. Measure the circumference of each circle by carefully positioning a string around the object’s base, then mark the place where the string ends meet. Measure the length in cm and record the measurements for each circle in Table 2.1. Repeat the procedure for each circle for three trials. Find the ratio of the circumference of each circle to its diameter. Fill the ratio for each trial in Table 2.1.
4. The ratio of the circumference of a circle to its diameter is known as pi (symbol π), which has a value of about 3.14. Compare your ratio with 3.14. Are they close?
| TABLE 2.1 Circles and Ratios | |||||||||
| Small Circle | Medium Circle | Large Circle | |||||||
| Trial | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 |
| Diameter (D) | 5.5 | 5.4 | 5.5 | 8.7 | 8.5 | 8.6 | 12.5 | 12.4 | 12.3 |
| Circumference (C) | 18.0 | 18.3 | 17.8 | 24.7 | 27.1 | 27.6 | 38.9 | 38.6 | 38.7 |
| Ratio of C/D | |||||||||
| Average C/D = _________________________________ |
Part B: Area and Volume Ratios
1. You will be given three cubes with different size. Note that a cube has six sides, or six units of
surface area. The side of a cube is also called a face, so each cube has six identical faces with the
same area. The overall surface area of a cube can be found by measuring the length and width of one
face (which should have the same value) and then multiplying (length)X(width)X(number of faces).
Use a metric ruler to measure the cube, then calculate the overall surface area and record your
finding for this each cube in Table 2.2.
2. The volume of a cube can be found by multiplying the (length)(width)(height). Measure and
calculate the volume of the cube and record your finding for each cube in Table 2.2.
3. Calculate the ratio of surface area to volume for each cube and record it in Table 2.2.
4. You only need calculate the surface area, the volume, and the ratio of surface area to the volume
of each cube.
5. Is there a trend or a pattern, or generalization, concerning the volume of a cube and its surface area to volume ratio. For example, as the volume of a cube increases, what happens to the surface area to volume ratio?
| TABLE 2.2 Area and Volume Ratios | |||
| Small Cube | Medium Cube | Large Cube | |
| Length of side (cm) | 2 cm | 4 cm | 6 cm |
| Surface Area, cm2 | |||
| Volume (cm3) | |||
| Ratio of Area/Volume | ________(cm2)/(cm3) | _________(cm2)/(cm3) | ________(cm2)/(cm3) |
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