Question

these solids are similar. find the surface area of the larger solid. h = 10 m sa = ? m² h = 5 m sa = 120 m²

Explanation:

Step1: Find the ratio of the heights

The ratio of the heights of the larger solid to the smaller solid is \(\frac{h_{1}}{h_{2}}=\frac{10}{5} = 2\).

Step2: Use the ratio of surface areas for similar solids

For similar solids, if the ratio of corresponding linear dimensions (such as height) is \(k\), the ratio of their surface areas is \(k^{2}\). Here \(k = 2\), so the ratio of the surface area of the larger solid (\(SA_{1}\)) to the surface area of the smaller solid (\(SA_{2}\)) is \(k^{2}=4\).
We know that \(\frac{SA_{1}}{SA_{2}}=k^{2}\). Given \(SA_{2} = 120\space m^{2}\) and \(k^{2}=4\), then \(SA_{1}=k^{2}\times SA_{2}\).
Substitute the values: \(SA_{1}=4\times120\).

Answer:

\(480\space m^{2}\)