Question
A cylindrical tank has a radius of 7 meters and a height
of 24 meters. A cone is placed inside the tank such that it touches the bottom and the sides of the tank. The cone has a height of 24 meters and the same radius as the cylinder. Find the volume of the space left in the tank after placing the cone.Solution
Volume of the cylinder = πr²h, Given: r = 7 meters, h = 24 meters. Volume of the cylinder = π(7)² (24) Volume of the cylinder = π × 49 × 24 Volume of the cylinder = 1176π m³. Volume of the cone = (1/3)πr²h, Volume of the cone = (1/3)π(7)²(24) Volume of the cone = (1/3)π × 49 × 24 Volume of the cone = 392π m³. Remaining volume = Volume of the cylinder - Volume of the cone Remaining volume = 1176π - 392π Remaining volume = 784π m³. Correct option: C) 784π m³
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