Question

the solids are similar. find the surface area of solid b to the nearest hundredth.
cylinder a
cylinder b
24 mm
16 mm
s = 594π mm²
the surface area of solid b is square millimeters

Explanation:

Step1: Find the ratio of the corresponding linear dimensions

The ratio of the heights of the two similar cylinders (since they are similar, the ratio of any corresponding linear dimensions can be used). Let the ratio be \(r\). For cylinder \(A\) with height \(h_A = 24\) mm and cylinder \(B\) with height \(h_B=16\) mm, \(r=\frac{h_B}{h_A}=\frac{16}{24}=\frac{2}{3}\).

Step2: Use the ratio of surface - areas formula for similar solids

The formula for the ratio of the surface areas of two similar solids is \(\frac{S_B}{S_A}=r^{2}\), where \(S_A\) is the surface area of solid \(A\) and \(S_B\) is the surface area of solid \(B\).
We know that \(S_A = 594\pi\) \(mm^{2}\) and \(r=\frac{2}{3}\). Substituting into the formula \(\frac{S_B}{594\pi}=(\frac{2}{3})^{2}\).

Step3: Solve for \(S_B\)

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Answer:

\(829.38\)