You purchased a scale model of the Statue of Liberty. The scale is 1:456. The model is 8 inches high and has a surface area of 0.052 ft^2.
a. What is the height of the Statue of Liberty?
b. What is the surface area of the Statue of Liberty?
Thanks for helping!
a. 456/1 = x/8
b. 456/1 = x/.052
Solve for x.
To find the height and surface area of the actual Statue of Liberty, we can use the scale ratio provided and the measurements of the scale model.
a. To find the height of the Statue of Liberty, we can use the scale ratio. The scale ratio of 1:456 means that every inch on the scale model represents 456 inches on the actual Statue of Liberty. Since the scale model is 8 inches high, we can multiply 8 by 456.
Hence, the height of the Statue of Liberty is 8 inches * 456 = 3,648 inches.
b. To find the surface area of the Statue of Liberty, we need to use the surface area of the scale model and scale ratio. The scale ratio applies to all dimensions, so the surface area of the scale model can be used as a reference.
The surface area of the scale model is 0.052 ft^2. Since the scale ratio is 1:456, we need to square the ratio to find the relationship between the surface areas.
(1:456) * (1:456) = (1/456) * (1/456) = 1/207,936
To find the surface area of the actual Statue of Liberty, we multiply the surface area of the scale model by the squared ratio:
Surface area of the actual Statue of Liberty = 0.052 ft^2 * (1/207,936)
Hence, the surface area of the Statue of Liberty is approximately 0.0000002497 square feet.