The volumes of two similar figures are given. The surface area of the smaller figure is given. Find the surface area of the larger figure.
Upper Vequals621 m cubed
Upper Vequals184 m cubed
S.A.equals224 m squared
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Part 1
The surface area of the larger figure is
enter your response here m squared.
To find the surface area of the larger figure, we will use the fact that the ratio of the volumes of similar figures is equal to the cube of the ratio of their corresponding sides, and that the ratio of surface areas of similar figures is equal to the square of the ratio of their corresponding sides.
Let x be the scale factor between the two figures. We can set up the following proportion:
\( \frac{(621)^{1/3}}{(184)^{1/3}} = \frac{S.A_{\text{larger}}}{224} \)
Solving for S.A_{larger}, we get:
\( S.A_{\text{larger}} = 224 \times (\frac{621}{184})^{2/3} \)
\( S.A_{\text{larger}} ≈ 439.35 \, \text{m}^2 \)
Therefore, the surface area of the larger figure is approximately 439.35 square meters.