Question

these solids are similar. find the volume of the smaller solid. r = 5 cm v = ? cm³ r = 6 cm v = 432 cm³

Explanation:

Step1: Find the ratio of the radii

The ratio of the radii of the smaller cylinder to the larger cylinder is \(\frac{r_{1}}{r_{2}}=\frac{5}{6}\).

Step2: Use the volume ratio formula for similar solids

For similar solids, the ratio of their volumes is \((\frac{r_{1}}{r_{2}})^3\). Let \(V_1\) be the volume of the smaller cylinder and \(V_2 = 432\space cm^3\) be the volume of the larger cylinder. Then \(\frac{V_1}{V_2}=(\frac{5}{6})^3\).

Step3: Solve for \(V_1\)

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Answer:

\(250\space cm^3\)