A conical vessel whose internal base radiusis 18 cm and height 60 cm is full of a liquid The entire ...........

Quantitative Aptitude (CPO) Mensuration 2D

A conical vessel whose internal base radiusis 18 cm and height 60 cm is full of a liquid. The entire liquid of the vessel is emptied into

a cylindrical vessel with internal radius 15 cm. The height (in cm) to which theliquid rises in the cylindrical vessel is:

This questions was previously asked in

SSC CPO 12th Dec 2019 Shift-1

28.8 cm

30.2 cm

27 cm

24 cm

To solve the problem, we need to follow these steps:

- Calculate the volume of the conical vessel:

- Formula: \( V = \frac{1}{3} \pi r^2 h \)

- Here, \( r = 18 \) cm and \( h = 60 \) cm.

- Volume = \(\frac{1}{3} \times \pi \times 18^2 \times 60\).

- Calculate the volume of liquid displaced in the cylindrical vessel:

- Let the height of the liquid in the cylindrical vessel be \(H\).

- Formula: \( V = \pi r^2 H \)

- Here, \( r = 15 \) cm.

- Equate the volumes to find \(H\).

- Use the volume relation:

- \(\frac{1}{3} \times \pi \times 18^2 \times 60 = \pi \times 15^2 \times H\).

- Simplifying gives \(H = 28.8\) cm.

- Conclusion:

- Option 1: 28.8 cm is the correct answer.

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