Question

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ratios and proportions
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kamal made a replica of the kaaba located in mecca, saudi arabia. the dimensions of his replica are 24 cm long by 21 cm wide by 30 cm high.
what is the surface area of the actual kaaba in meters if the scale factor is 50?
enter your answer as a whole number, with the appropriate unit, like this: 42 m^2

Explanation:

Step1: Calculate surface - area of the replica

The replica is a rectangular prism. The surface - area formula for a rectangular prism is $SA = 2(lw+lh + wh)$, where $l = 24$ cm, $w = 21$ cm, and $h = 30$ cm.
$SA_{replica}=2(24\times21 + 24\times30+21\times30)$
$=2(504 + 720+630)$
$=2\times1854$
$=3708$ $cm^{2}$

Step2: Find the surface - area of the actual Kaaba

If the scale factor is $k = 50$, the ratio of the surface - areas of two similar solids is $k^{2}$.
The surface - area of the actual Kaaba $SA_{actual}=k^{2}\times SA_{replica}$
$SA_{actual}=50^{2}\times3708$
$=2500\times3708$
$=9270000$ $cm^{2}$

Step3: Convert the unit from $cm^{2}$ to $m^{2}$

Since $1$ m = $100$ cm, $1$ $m^{2}=10000$ $cm^{2}$.
$SA_{actual}=\frac{9270000}{10000}=927$ $m^{2}$

Answer:

$927$ $m^{2}$