To find the height of a pyramid, we can use the formula for the volume of a pyramid, which is:
\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \]
Where:
- \( V \) is the volume of the pyramid.
- The base area is the area of the base of the pyramid.
- The height (\( h \)) is the perpendicular distance from the base to the apex.
We are given the following values:
- The base area is 70 square units.
- The volume (\( V \)) is 140 cubic units.
Let's plug these values into the formula and solve for the height (\( h \)):
\[ 140 = \frac{1}{3} \times 70 \times h \]
To isolate \( h \), we multiply both sides of the equation by 3 and divide by the base area:
\[ h = \frac{3 \times 140}{70} \]
Now we simplify the right side of the equation:
\[ h = \frac{3 \times 140}{70} = \frac{420}{70} \]
\[ h = 6 \]
Therefore, the height of the pyramid is 6 units.
The correct answer is B) 6 units.
