Question

Cylinders A and B are similar solids. The base of cylinder A has a circumference of 4π units. The base of cylinder B has an area of 9π units.The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B?

Answer 1

The formula for the circumference of a circle is
C = 2π·r
or
r = C/(2π)
The radius r of cylinder A is
r = (4π)/(2π) = 2

The formula for the area of a circle is
A = π·r²
or
r = √(A/π)
The radius of cylinder B is
r = √(9π/π) = 3

The dimensions of cylinder A must be multiplied by 3/2 to produce the corresponding dimensions of cylinder B.

Answer 2

A has a radius of 2 (4pi/pi = 4 diameter, 4/2 = 2 radius)
B has a radius of 3 (9pi/pi = 9, 9 is r squared, so the sqrt of 9 is 3)
A * x = B
2 * x = 3
x = 3/2
The answer is C), 3/2