Posted by Anonymous on .
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?
Solve and proof, following problem solving rubric.

Geometry Help & Proofs 
Reiny,
based on :
ratio of volumes is proportional to the cube of their corresponding sides.
so ratio of volumes:
A : B = 1 : 5
A : C = 1^3 : 2^3 = 1 : 8
B : D = 1^3 : 3^3 = 1 : 27
A/B = 1/5
B = 5A
A/C = 1/8
C = 8A
B/D = 1/27
D = 27B
ratio of volume of C :D
= 8A : 27B
= (8/27)(A/B)
= (8/27)((1/5)
= 8 : 135
check my arithmetic