Farina wrote:
Right circular cylinders A and B have equal volumes. Cylinder A has a radius of x, and cylinder B has a radius of 2x.
Quantity A |
Quantity B |
The height of Cylinder A |
Twice the height of Cylinder B |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
The formula for volumes of cylinders, rectangular solids and prisms is the product of their height and base area or \(h \cdot A\), where \(h\) is there height and \(A\) is their area, respectively.
Since a cylinder is a circle as its base, the area of its base is \(\pi r^2\) and its volume is \(\pi r^2 h\), where \(h\) and \(r\) are its height and radius, respectively.
Since cylinder \(A\) has a radius of \(x\), cylinder \(B\) has a radius of \(2x\) and they have equal volumes, we have \(\pi x^2 h_A = \pi (2x)^2 h_B\) or \(h_A = 4h_B\), where \(h_A\) and \(h_B\) are heights of those two cylinders.
Since \(h_A = 4h_B > 2h_B\), we have \(A > B\).
Therefore, A is the right answer.