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 answer:

p =  14:9

Step-by-step explanation:

$$\begin{gathered} p_1={\displaystyle \frac{7}{8}}=0.875 \\ {p}_2={\displaystyle \frac{4}{3}}\doteq 1.3333 \\ {p}_1=h_1:h_2 \\ {p}_2=r_1:r_2 \\ {V}_1=\pi r_1^2{h}_1 \\ {V}_2=\pi r_2^2{h}_2 \\ {V}_1=\pi \cdot (p_2\cdot r_2{)}^2\cdot (p_1\cdot h_2) \\ {V}_1=\pi \cdot p_2^2\cdot r_2^2\cdot p_1\cdot h_2=p_2^2\cdot p_1\cdot V_2 \\ p=V_1\mathrm{/}{V}_2 \\ p=p_2^2\cdot p_1=1.3333^2\cdot 0.875={\displaystyle \frac{14}{9}}=1\frac{5}{9}\approx 1.5556=14:9 \end{gathered}$$

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