Physical Geology

Step 1: Understanding the scale.
The scale of the map is 1:50000, meaning 1 cm on the map corresponds to 50000 cm (or 500 meters) on the ground. To convert the actual length of the dyke to the map length, we divide the actual length by the scale.

Step 2: Calculation.
The actual length of the dyke is 2 km, which is 2000 meters. The map length is calculated as:

Step 3: Conclusion.
The length of the dyke on the map is 4.0 cm.

Step 1: Formula for rate of change.
For a sphere, . Step 2: Convert radius.

Step 3: Substitute.
Step 4: Round off.
5.02 ×10^–7 cm = 5.02 ×10^–8 (in given format).

Step 1: Formula used.
Density ( ) = Mass / Volume.
Volume = .
Step 2: Substitution.
Mass = 200 g = 0.2 kg, .
Step 3: Cube length.
Step 4: Conclusion.
The cube’s edge length = 40 mm.