standard_description: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
problem_activity: In science class, you measure the mass and volume of different pieces of aluminum. You determine that there is a proportional relationship between mass and volume. The data on four samples of aluminum is shown in the table.
{"table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "table-layout:Fixed; width:50%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$^3$$"}], "_values": ["Volume (cm", ")"]}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Mass (g)"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "4"}, {"_attributes": {"style": "text-align:center"}, "_value": "10.8"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "7"}, {"_attributes": {"style": "text-align:center"}, "_value": "18.9"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "12"}, {"_attributes": {"style": "text-align:center"}, "_value": "32.4"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "18"}, {"_attributes": {"style": "text-align:center"}, "_value": "48.6"}]}]}]}]}
After you put your scale away, you realize that you forgot to find the mass of one more piece of aluminum. The volume of the piece of aluminum is 10 cm
$${^3}$$
. Can you determine the mass without taking your scale back out?


aligns: no