Question

an architect designs a castle tower for a new attraction at a popular amusement park. blueprints of the tower, which is in the shape of a rectangular prism, show that it is 47 cm tall, 23 cm in length, and 25 cm in width. the blueprints have a scale factor of 1:96. calculate the actual surface area of the tower. enter your answer as a number, rounded to hundredths, with the appropriate unit, like this: 42.53 m^2

Explanation:

Step1: Find actual dimensions

Multiply blueprint dimensions by scale - factor.
Actual height $h = 47\times96 = 4512$ cm, actual length $l = 23\times96=2208$ cm, actual width $w = 25\times96 = 2400$ cm.

Step2: Use surface - area formula for rectangular prism

The surface - area formula of a rectangular prism is $SA=2(lw + lh+wh)$.
$SA = 2(2208\times2400+2208\times4512 + 2400\times4512)$
First, calculate each product:
$2208\times2400 = 5299200$
$2208\times4512=2208\times(4000 + 500+12)=2208\times4000+2208\times500+2208\times12=8832000+1104000 + 26496=9962496$
$2400\times4512 = 10828800$
Then, add them:
$5299200+9962496+10828800 = 26090496$
Multiply by 2:
$SA = 2\times26090496=52180992$ $cm^{2}$

Step3: Convert to square meters

Since $1$ m = $100$ cm, $1$ $m^{2}=10000$ $cm^{2}$.
$SA=\frac{52180992}{10000}=5218.10$ $m^{2}$

Answer:

$5218.10$ $m^{2}$