Final answer:
The actual depth of the scratch on the Earth's surface, represented by a 0.1 cm deep scratch on a classroom globe with a 20 cm diameter, is 63.5 km after applying the scale factor derived from Earth's actual diameter.
Step-by-step explanation:
To find the actual depth of the surface feature on the real Earth represented by a scratch made on a classroom globe, we need to apply a scale factor based on the size of the globe compared to the actual size of Earth. The scratch is 0.1 cm deep on a globe with a diameter of 20 cm. Since the actual diameter of Earth is about 12,700 km, we calculate the scale factor as the diameter of the Earth divided by the diameter of the globe, which is 12,700 km / 20 cm.
Converting kilometers to centimeters, we have 12,700 km is equal to 1,270,000,000 cm. Therefore, the scale factor is 1,270,000,000 cm / 20 cm = 63,500,000. To find the actual depth of the scratch, we multiply the depth of the scratch on the globe by the scale factor, which is 0.1 cm × 63,500,000 = 6,350,000 cm or 63.5 km.
To calculate the actual depth of the scratch on the real Earth, first, we need to find the scale factor between the classroom globe and the real Earth. Using the diameter of the classroom globe (20 cm) and the actual diameter of the Earth (12,700 km), we can calculate the scale factor as:
Scale Factor = Actual Earth Diameter / Globe Diameter = (12,700 km) / (20 cm)
Next, we multiply the scale factor by the depth of the scratch on the globe (0.1 cm) to find the actual depth on the real Earth:
Actual Depth = Scale Factor * Globe Depth = Scale Factor * 0.1 cm
Plugging in the values, we get:
Actual Depth = (12,700 km / 20 cm) * 0.1 cm