Discussion
The height and base radius of a right circular cylinder are 9 cm and 6 cm respectively. If the base radius becomes half and height increases by 3 cm, then which of the following describes the new volume of the cylinder ?
Answer: D
The new volume is one-third of the original volume.
\[ \begin{aligned} V_1 &= \pi r^2 h = \pi (6)^2 (9) = 324\pi \\ V_2 &= \pi (3)^2 (12) = 108\pi \\ \frac{V_2}{V_1} &= \frac{108}{324} = \frac{1}{3} \end{aligned} \]
Halving the radius divides the volume by 4, because volume depends on the square of the radius, while raising the height from 9 to 12 multiplies it by 4/3; together the factor is 1/3. Choosing 'half' comes from treating the radius as if it entered the volume linearly.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development