Two similar rectangular prisms have corresponding sides that measure 5 feet and 6 feet. If the measures of two corresponding sides of two similar solids are 3 meters and 5 meters, what is the ratio of the surface areas of the solids?
A1/A2 = (3/5)^2 = 0.36.
To find the ratio of the surface areas of two similar solids, we need to compare the squares of the corresponding sides.
Let's call the ratio of the corresponding sides of the first pair of similar rectangular prisms as "x" and the ratio of the corresponding sides of the second pair as "y".
Given:
x = 5 feet / 6 feet
y = 3 meters / 5 meters
To find the ratio of the surface areas, we square the ratios x and y:
x^2 = (5/6)^2
y^2 = (3/5)^2
Calculating x^2 and y^2:
x^2 = 25/36
y^2 = 9/25
The ratio of the surface areas would be:
x^2 : y^2 = (25/36) : (9/25)
Now, we simplify this ratio by multiplying both sides by the least common multiple (LCM) of the denominators:
LCM(36, 25) = 900
(25/36) : (9/25) = (25/36) * (25/25) : (9/25) * (36/36)
= (625/900) : (324/900)
Therefore, the ratio of the surface areas of the two similar solids is:
625 : 324
To find the ratio of the surface areas of two similar solids, we can use the fact that the ratio of the surface areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.
In this case, the corresponding side lengths of the two similar solids are 3 meters and 5 meters. So, the ratio of their side lengths is 3:5.
To find the ratio of their surface areas, we square this ratio:
(3:5)^2 = 9:25
Therefore, the ratio of the surface areas of the two similar solids is 9:25.