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

(a) 1/3 ✓ UPSC's answer
(b) 1/2
(c) 1/4
(d) 1/6

Why the answer is (a)

• Calculate the volume of the cylindrical overhead tank using the formula V = πr²h, where r = 2 m and h = 7 m, resulting in 28π cubic meters.

• Approximate π as 22/7 to simplify the calculation, giving a volume of 28 × (22/7) = 88 cubic meters.

• Calculate the total volume of the underground rectangular tank using the formula V = length × width × height, which is 5.5 × 4 × 6 = 132 cubic meters.

• Determine the volume of water remaining in the underground tank by subtracting the overhead tank's volume from the total: 132 - 88 = 44 cubic meters.

• Calculate the fraction of the underground tank still filled by dividing the remaining volume by the total volume: 44 / 132 = 1/3.

• Therefore, the portion of the underground tank still filled with water is 1/3, which corresponds to option (a).

Why the other options are wrong

(b) 1/2: Option (b) 1/2 implies 66 cubic meters remain, which would require the overhead tank to hold only 66 cubic meters, contradicting the calculated volume of 88 cubic meters.
(c) 1/4: Option (c) 1/4 implies 33 cubic meters remain, which would require the overhead tank to hold 99 cubic meters, which is incorrect based on the dimensions provided.
(d) 1/6: Option (d) 1/6 implies 22 cubic meters remain, which would require the overhead tank to hold 110 cubic meters, which is incorrect based on the dimensions provided.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.