A cylindrical overhead tank of radius 2m and height 7m is to be filled from an underground tank of size 5.5m × 4m × 6m. How much portion of the underground tank is still filled with water after filling the overhead tank completely?

Correct Option (1)

To determine the portion of the underground tank that remains filled, the volumes of both tanks must first be calculated.

• The volume of the cylindrical overhead tank is calculated using the formula $V=\pi r^{2}h$. Given a radius \(r = 2\) m and a height \(h = 7\) m, the volume is:

$$V_{\text{cylindrical}}=\frac{22}{7}\times (2{)}^2\times 7=\frac{22}{7}\times 4\times 7=88{\text{ m}}^3$$

• The volume of the cuboidal underground tank is calculated using the formula $V=\text{length}\times \text{width}\times \text{height}$. Given dimensions of 5.5 m, 4 m, and 6 m, the volume is:

$$V_{\text{underground}}=5.5\times 4\times 6=132{\text{ m}}^3$$

• After the overhead tank is filled completely, the volume of water remaining in the underground tank is:

$$V_{\text{remaining}}=V_{\text{underground}}-V_{\text{cylindrical}}=132-88=44{\text{ m}}^3$$

• The portion of the underground tank still filled with water is the ratio of the remaining volume to the original volume of the underground tank:

$$\text{Portion}=\frac{V_{\text{remaining}}}{V_{\text{underground}}}=\frac{44}{132}=\frac{1}{3}$$

Incorrect Options:

Options 2, 3, and 4 are incorrect because the precise calculation of the volumes and the subsequent ratio of the remaining water to the initial volume of the underground tank yields $1/3$.