Question
Download Solution PDFThe 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 (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
The formula for the volume of a right circular cylinder is: V = πr²h, where r is the base radius and h is the height.
Original radius (r) = 6 cm
Original height (h) = 9 cm
Calculation:
Original Volume (Voriginal) = π × (6)² × 9 = π × 36 × 9 = 324π cm³
New Dimensions of the Cylinder:
New radius = 6 cm / 2 = 3 cm
New height = 9 cm + 3 cm = 12 cm
New Volume of the Cylinder:
New Volume (Vnew) = π × (3)² × 12 = π × 9 × 12 = 108π cm³
Now, we need to compare the new volume with the original volume:
Comparing Volumes:
Original Volume (Voriginal) = 324π cm³
New Volume (Vnew) = 108π cm³
New Volume / Original Volume = 108π / 324π = 1/3
Thus, the new volume is one-third of the original volume.
∴ The Correct answer is Option (2): The new volume will be one-third the original volume.
Last updated on Apr 30, 2025
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