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.
Since each pillar has a total height of 10 units, subtract the visible height from 10 to find the buried height:
Pillar 1: 10 - 7 = 3 units
Pillar 2: 10 - 5 = 5 units
Pillar 3: 10 - 3 = 7 units
Pillar 4: 10 - 6 = 4 units
Pillar 5: 10 - 9 = 1 unit
3. Calculate the Total Visible Height:
7 + 5 + 3 + 6 + 9 = 30 units
4. Calculate the Total Buried Height:
3 + 5 + 7 + 4 + 1 = 20 units
5. Determine the Ratio:
The ratio of the total volume above the ground to the total volume below the ground is the same as the ratio of their heights because they have equal cross sections.
This ratio is 30:20, which simplifies to 3:2.
Therefore, the ratio of the total volume of the pillars above and below the ground is 3:2.
