Five identical pillars, having equal height of 10 units and equal cross section, are inserted into the ground. Figure C shows only the portions of the pillars visible above ground. Which of the options given below indicates the ratio of the total volume of the pillars above and below the ground?
Show Hint
To solve ratio-based volume problems, always sum up the individual visible and hidden portions before calculating the ratio. Identifying patterns in the given structure can help simplify the calculations.
Step 1: Analyze the given information about the pillars. Each pillar has a total height of 10 units, but part of it is inserted into the ground, leaving only some portion visible above ground.
Step 2: Identify the heights of the visible parts from Figure C:
- First pillar: 5 units above
- Second pillar: 4 units above
- Third pillar: 2 units above
- Fourth pillar: 5 units above
- Fifth pillar: 6 units above
Step 3: Calculate the total visible height:
\[
5 + 4 + 2 + 5 + 6 = 22 \text{ units}
\]
Since each pillar is 10 units tall and there are 5 pillars, the total height of all pillars is:
\[
10 \times 5 = 50 \text{ units}
\]
The portion below the ground is:
\[
50 - 22 = 28 \text{ units}
\]
Step 4: Compute the ratio of above-ground volume to below-ground volume:
\[
22:28 = 1:1
\]
Thus, the correct answer is option C (\( 1:1 \)).
