Question

these solids are similar. find the surface area of the smaller solid. h = 4 m sa =? m² h = 10 m sa = 250 m²

Explanation:

1. Recall the ratio - of - surface - areas for similar solids:

• For two similar solids, if the ratio of their corresponding linear dimensions (such as heights) is \(a:b\), the ratio of their surface - areas is \(a^{2}:b^{2}\).
• Let the height of the larger solid be \(h_1 = 10m\) and its surface - area be \(SA_1=250m^{2}\), and the height of the smaller solid be \(h_2 = 4m\) and its surface - area be \(SA_2\).
• The ratio of the heights is \(\frac{h_2}{h_1}=\frac{4}{10}=\frac{2}{5}\).
• The ratio of the surface - areas of the two similar solids is \((\frac{h_2}{h_1})^2\). So, \(\frac{SA_2}{SA_1}=(\frac{h_2}{h_1})^2\).

1. Substitute the known values into the formula:

• Substitute \(h_1 = 10\), \(h_2 = 4\), and \(SA_1 = 250\) into the equation \(\frac{SA_2}{SA_1}=(\frac{h_2}{h_1})^2\).
• \(\frac{SA_2}{250}=(\frac{4}{10})^2=\frac{16}{100}\).
• Cross - multiply to solve for \(SA_2\): \(SA_2=\frac{16\times250}{100}\).
• First, calculate \(16\times250 = 4000\). Then, \(\frac{4000}{100}=40\).

Answer:

\(40\)