A solid metal cube of edge 12 cm is immersed completely in water in a cylindrical vessel whose radiu...........

Quantitative Aptitude (MTS) Mensuration 2D

A solid metal cube of edge 12 cm is immersed completely in water in a cylindrical vessel whose radius is 20 cm and height is 32

cm, and the water in the vessel is up to a height of 15 cm. The height (in cm) by which the water will rise in the vessel is (correct

to one decimal place):

This questions was previously asked in

SSC MTS 6th October 2021 Shift-3

0.9

1.4

1.2

1.1

- A solid metal cube with an edge of 12 cm is submerged in water.

- Volume of the cube = side³ = 12 cm × 12 cm × 12 cm = 1,728 cm³.

- This volume of the cube will displace an equal volume of water in the cylindrical vessel.

- The vessel's cross-sectional area = p × radius² = p × (20 cm)² = 400p cm².

- Rise in water height = displaced volume / vessel's cross-sectional area = 1,728 cm³ / 400p cm².

- Rise = 1,728 / (400p) = 1,728 / (1,256.64) = approximately 1.4 cm.

- Correct Answer: Option 2: 1.4

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