Question

these prisms are similar. find the surface area of the larger prism. round to the nearest tenth. 5 in. 6 in. surface area = 572 m² surface area = ? m²

Explanation:

Step1: Recall ratio of surface - areas of similar solids

For two similar solids with a scale factor of \(a:b\), the ratio of their surface - areas is \(a^{2}:b^{2}\). Here, the scale factor of the two prisms is \(5:6\), so the ratio of their surface - areas is \(5^{2}:6^{2}=25:36\).

Step2: Set up a proportion

Let \(S\) be the surface area of the larger prism. We have the proportion \(\frac{25}{36}=\frac{572}{S}\).

Step3: Cross - multiply and solve for \(S\)

Cross - multiplying gives us \(25S = 36\times572\). Then \(S=\frac{36\times572}{25}\).
\[S=\frac{20592}{25}=823.68\]

Step4: Round to the nearest tenth

Rounding \(823.68\) to the nearest tenth gives \(823.7\).

Answer:

\(823.7\ m^{2}\)