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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