# Geometry Help & Proofs

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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 -

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

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