IAS 2016 — CSAT Maths

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 $V = \pi r^2 h$V=πr2h. Given a radius $r = 2$r=2 m and a height $h = 7$h=7 m, the volume is:

$$V_{\text{cylindrical}} = \frac{22}{7} \times (2)^2 \times 7 = \frac{22}{7} \times 4 \times 7 = 88 \text{ m}^3$$Vcylindrical​=722​×(2)2×7=722​×4×7=88 m3

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

$$V_{\text{underground}} = 5.5 \times 4 \times 6 = 132 \text{ m}^3$$Vunderground​=5.5×4×6=132 m3

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

$$V_{\text{remaining}} = V_{\text{underground}} - V_{\text{cylindrical}} = 132 - 88 = 44 \text{ m}^3$$Vremaining​=Vunderground​−Vcylindrical​=132−88=44 m3

• 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:

$$\text{Portion} = \frac{V_{\text{remaining}}}{V_{\text{underground}}} = \frac{44}{132} = \frac{1}{3}$$Portion=Vunderground​Vremaining​​=13244​=31​

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$1/3.