Question

a statue that is 80 m tall stands on a 625 m² base. an artist creates a replica using a ratio of 1:15. what is the area of the replicas base? 5.33 m² 2.78 m² 9375 m² 41.67 m²

Explanation:

Step1: Recall ratio - area relationship

If the linear - scale ratio of two similar figures is \(a:b\), the ratio of their areas is \(a^{2}:b^{2}\). Here, the linear - scale ratio of the statue and its replica is \(1:15\), so the ratio of the area of the replica's base to the area of the original base is \((1)^{2}:(15)^{2}=1:225\).

Step2: Set up proportion

Let \(A\) be the area of the replica's base. We have the proportion \(\frac{A}{625}=\frac{1}{225}\).

Step3: Solve for \(A\)

Cross - multiply to get \(225A = 625\). Then \(A=\frac{625}{225}=\frac{25}{9}\approx2.78\mathrm{m}^{2}\).

Answer:

\(2.78\mathrm{m}^{2}\)