QUESTION

CSAT

Hard

Maths

Prelims 2016

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 × 6 m. How much portion of the underground tank is still filled with water after filling the overhead tank completely?

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Explanation

Step 1: Find the Volume of the Overhead Tank Formula: $V = \pi r^2 h$ Radius (r) = 2, Height (h) = 7 $V = \pi \cdot (2)^2 \cdot 7 = 28\pi \approx 87.92$ m³

Step 2: Find the Volume of the Underground Tank Formula: $V = L \cdot B \cdot H$ Length (L) = 5.5, Breadth (B) = 6, Height (H) = 4 (assuming full initially) $V = 5.5 \cdot 6 \cdot 4 = 132$ m³

Step 3: Find the Remaining Portion of Water in the Underground Tank Volume of water used = Volume of overhead tank = 87.92 m³ Remaining Volume = $132 - 87.92 = 44.08$ m³