Cuboid immersed in a cylinder
A right circular hollow cylinder of internal volume 540 cm3 and internal base radius 3 cm, contains water of volume 162 cm3. A cuboid having square base area 9 cm2 and height 10 cm is placed into the cylinder, with its square base resting completely on the base of the cylinder. What is the increase in the height of water. (Take π (pi) as 3 , Ignore the width of the cylinder)
3 cm
10/3 cm
9 cm
None of the above.
Cannot be determined.
Answer :3 cm
Solution (Fast Approach)
Volume of water = 162 cm3. Height of water level : 162/π*3*3 = 6 cm
Height of the cuboid = 10 cm. Cuboid may not immerse fully in the cylinder.
Let us assume the final height of the water = X
Volume of cuboid inside the water = base area * height = 9X
Volume of the portion of the cylinder, till the water level of height X. = 27X
Final Volume after increase in height of water = volume of immersed cuboid + volume of water
27 X = 9 X + 162
X = 162/18 = 9 cm
Hence the increase in the height of the water = 9 - 6 = 3 cm
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