The radius of a cylinder is reduced to 50 of its actual radius If its volume remains the same as bef...........

Quantitative Aptitude (MTS) Mensuration 3D

The radius of a cylinder is reduced to 50% of its actual radius. If its volume remains the same as before, then its height

becomes k times the original height. The value of k is:

This questions was previously asked in

SSC MTS 14th October 2021 Shift-3

- The volume of a cylinder is given by V = pr²h, where r is the radius and h is the height.

- If the radius is reduced to 50%, the new radius = r/2.

- Let the new height be h'.

- The new volume V' = p(r/2)² × h' = p(r²/4) × h' = (pr²h') / 4.

- Since the volume stays the same: V' = V ? (pr²h') / 4 = pr²h

- Divide both sides by pr²: h'/4 = h ? h' = 4h.

- So, the new height becomes 4 times the original height.

- Among the options:

- Option 1: 2 – Incorrect.

- Option 2: 16 – Incorrect.

- Option 3: 8 – Incorrect.

- Option 4: 4 – Correct.

Submit Error