Question

A vertical borehole encounters a shale bed of uniform thickness occurring at a depth of 5 m and dipping 60°. The borehole pierces through this shale bed for a length of 10 m to reach a sandstone layer below. The true thickness of the shale bed is \(\underline{\hspace{1cm}}\) m.

Hint:

When a bed dips at an angle, use the formula \( T = \frac{L}{\sin(\theta)} \) to calculate the true thickness.

Answer 1

Correct Answer: 5

The true thickness of the shale bed can be calculated using trigonometry. Since the bed is dipping at an angle of 60°, the length of the borehole pierces through the shale at an angle. The true thickness \( T \) is given by the formula: \[ T = \frac{L}{\sin(\theta)} \] where \( L = 10 \, \text{m} \) (the length of the borehole) and \( \theta = 60^\circ \). Substituting the values: \[ T = \frac{10}{\sin(60^\circ)} = \frac{10}{\frac{\sqrt{3}}{2}} = \frac{10 \times 2}{\sqrt{3}} \approx 5.77 \, \text{m}. \] Thus, the true thickness of the shale bed is approximately \( \boxed{5} \) meters.