The ratio of the volume of Cylinder A to the volume of Cylinder B is 1:5. Cylinder A is similar to Cylinder C with a scale factor of 1:2 and Cylinder B is similar to Cylinder D with a scale factor of 1:3. What is the ratio of the volume of Cylinder C to the volume of Cylinder D?
the radii are in the ratios of
A/C = 1/2
B/D = 1/3
so the volumes are in the ratio of
A/B = 1/5
A/C = 1/8
B/D = 1/27
So, we want C/D.
C/D = A/B * B/D * C/A
= 1/5 * 1/27 * 8/1 = 8/135
To find the ratio of the volume of Cylinder C to the volume of Cylinder D, we need to first find the individual ratios of the volumes of Cylinders A to C and B to D.
Given that the ratio of the volume of Cylinder A to the volume of Cylinder B is 1:5, we can assume the volumes as x and 5x respectively.
Now, since Cylinder A is similar to Cylinder C with a scale factor of 1:2, the ratio of their volumes will be (1^3):(2^3) or 1:8. Therefore, the volume of Cylinder C is 8x.
Similarly, Cylinder B is similar to Cylinder D with a scale factor of 1:3, so the ratio of their volumes will be (1^3):(3^3) or 1:27. Therefore, the volume of Cylinder D is 27(5x) = 135x.
To find the ratio of the volume of Cylinder C to the volume of Cylinder D, we divide the volume of Cylinder C by the volume of Cylinder D:
Volume of C / Volume of D = 8x / 135x
= 8/135
So, the ratio of the volume of Cylinder C to the volume of Cylinder D is 8:135 or 8/135.