The scale model of a building is 5.4 feet tall.
A)If the original building is 810 meters tall, what was the scale used to make the model?
B)If the model is made out of tiny bricks each measuring 0.4 inch in height, how many bricks tall is the model?
THANK YOU!!
A) To find the scale used to make the model, we can set up a proportion:
Let x be the scale used to make the model.
According to the problem, the scale model is 5.4 feet tall, and the original building is 810 meters tall.
Since 1 meter is equal to 3.28 feet, we can convert the height of the original building to feet:
810 meters * 3.28 feet/meter = 2656.8 feet
Now we can set up the proportion:
5.4 feet (height of the model) / x = 2656.8 feet (height of the original building) / 1
Cross-multiplying:
5.4 feet * 1 = x * 2656.8 feet
5.4 = 2656.8x
Dividing both sides by 2656.8:
5.4 / 2656.8 = x
x ≈ 0.002034
The scale used to make the model is approximately 0.002034.
B) To find how many bricks tall the model is, we can divide the total height of the model by the height of each individual brick.
The total height of the model is 5.4 feet, and each brick measures 0.4 inches in height.
Since 1 foot is equal to 12 inches, we need to convert the total height of the model to inches:
5.4 feet * 12 inches/foot = 64.8 inches
Now we can divide the total height of the model by the height of each brick:
64.8 inches / 0.4 inches/brick = 162 bricks
Therefore, the model is 162 bricks tall.
A) To find the scale used to make the model, we'll compare the height of the model to the height of the original building. We can set up a proportion using the heights:
Let's assign variables:
- Height of the model = M
- Height of the real building = B
- Scale used = S
According to the information given,
M = 5.4 feet
B = 810 meters
The scale represents the ratio between the model and the real building:
S = M/B
Substituting the given values:
S = 5.4 feet / 810 meters
Since we need to convert the units to either feet or meters to proceed with the calculation, let's convert the height of the real building to feet (since the model's height is already in feet).
1 meter = 3.281 feet (approximately)
Converting the height of the real building:
810 meters * 3.281 feet/meter = 2657.19 feet (approximately)
Now we can proceed with the proportion:
S = 5.4 feet / 2657.19 feet
Calculating the scale:
S ≈ 0.002031
Therefore, the scale used to make the model is approximately 0.002031.
B) To find out how many bricks tall the model is, we'll divide the height of the model by the height of a single brick.
Let's assign variables:
- Height of the model = M
- Height of a single brick = H
- Number of bricks tall = N
According to the information given,
M = 5.4 feet
H = 0.4 inches
The number of bricks tall can be calculated using the formula:
N = M / H
Substituting the given values:
N = 5.4 feet / 0.4 inches
However, we need to make sure that the units are consistent. Let's convert the height of the model to inches.
1 foot = 12 inches
Converting the height of the model:
5.4 feet * 12 inches/foot = 64.8 inches
Now we can proceed:
N = 64.8 inches / 0.4 inches
Calculating the number of bricks tall:
N = 162
Therefore, the model is approximately 162 bricks tall.
A) 1 foot = .3048 m
(5.4*.3048)/810 = ?
B) (5.4*12)/.4 = ?
A=.002032
B=163