Question

these solids are similar. find the volume of the larger solid. r = 3 cm v = ? cm³ r = 1 cm v = 9 cm³

Explanation:

Step1: Find the scale factor of the radii

The scale factor \(k\) of the radii is \(\frac{3}{1}=3\)

Step2: Use the volume ratio formula for similar solids

For similar solids, the ratio of volumes \(V_1\) and \(V_2\) is \(V_1:V_2 = k^{3}\). Let \(V_1\) be the volume of the larger cylinder and \(V_2 = 9\mathrm{cm}^3\) be the volume of the smaller cylinder.
Since \(k = 3\), then \(V_1=V_2\times k^{3}\)
Substitute \(V_2 = 9\) and \(k = 3\) into the formula: \(V_1=9\times3^{3}\)
Calculate \(3^{3}=27\), then \(V_1=9\times27\)
\(V_1 = 243\)

Answer:

\(243\mathrm{cm}^3\)