Ratio of volumes

If the heights of two cylindrical drums are in the ratio 7:8 and their base radii are in the ratio 4:3. What is the ratio of their volumes?

Correct result:

p =  14:9

Solution:

p1=78=0.875 p2=43≐1.3333  p1=h1:h2 p2=r1:r2  V1=πr12 h1 V2=πr22 h2  V1=π⋅ (p2⋅ r2)2⋅ (p1⋅ h2) V1=π⋅ p22⋅ r22⋅ p1⋅ h2=p22⋅ p1⋅ V2   p=V1/V2  p=p22⋅ p1=1.33332⋅ 0.875=149≈1.5556=14:9

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