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 and enter your answer in square meters with two decimal places, formatted like this: 42.53 m^2

Answer 1

Answer:

The surface area of the tower is 5,218.1 m²

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Height of the blueprint = 47 cm

Length of the blueprint = 23 cm

Width of the blueprint = 25 cm

Scale factor 1 : 96

2. Calculate the actual surface area of the tower and enter your answer in square meters with two decimal places.

Let's calculate the measurements of the actual tower:

Height of the blueprint = 47 * 96 = 4,512 cm = 45.12 m

Length of the blueprint = 23 * 96 = 2,208 cm = 22.08 m

Width of the blueprint = 25 * 96 = 2,400 cm = 24 m

Now, let's calculate the surface area of the tower, this way:

Surface area of the tower = 2* (24 * 22.08) + 2 * (45.12 * 22.08) + 2 * (45.12 * 24)

Surface area of the tower = 1,059.84 + 1,992.5 + 2,165.76

Surface area of the tower = 5,218.1 m²