what is the ratio of the surface areas for a pair of similar cylinders when the ratio of the heights is 1:3?
i don't understand this at all!!
the surface area of similar figures varies directly as the square of their corresponding sides
so surface area(1)/surface area(2) = (1^2)/(3^2) = 1/9
so the surface area of the larger cylinder is 9 times that of the smaller.
To understand the ratio of the surface areas for a pair of similar cylinders when the ratio of heights is 1:3, let's break it down step-by-step:
Step 1: Understand the ratio of the heights.
In this problem, we are given a ratio of 1:3 for the heights of the two cylinders. This means that the height of the larger cylinder is three times the height of the smaller cylinder.
Step 2: Find the relationship between the surface areas of similar objects.
For similar objects, the ratio of their surface areas is equal to the square of the ratio of their corresponding lengths (or heights in this case).
Therefore, the ratio of the surface areas of the two similar cylinders will be the square of the ratio of their heights.
Step 3: Apply the formula to find the ratio of surface areas.
Since the ratio of heights is 1:3, the square of this ratio will be (1/3)^2 = 1/9.
Therefore, the ratio of the surface areas of the two similar cylinders is 1:9.
In summary, the ratio of the surface areas for a pair of similar cylinders when the ratio of heights is 1:3 is 1:9.
To find the ratio of the surface areas for a pair of similar cylinders, you need to compare the areas of their curved surfaces. The curved surface area of a cylinder can be calculated using the formula:
Curved Surface Area = 2πrh
where "r" represents the radius of the cylinder's base and "h" represents the height of the cylinder.
In this case, you have two similar cylinders with a height ratio of 1:3. Let's assume the height of the first cylinder is "h1" and the height of the second cylinder is "h2" = 3h1.
Now, let's find the ratio of the surface areas using the formula mentioned above:
Ratio of Surface Areas = (Curved Surface Area of Cylinder 1) / (Curved Surface Area of Cylinder 2)
Since the radius of both cylinders is not mentioned and the ratio of heights doesn't tell us anything about the radii, we can assume that the radii are equal. Hence, we can cancel out the radius to simplify the formula:
Ratio of Surface Areas = (2πr * h1) / (2πr * h2) = h1 / h2
Substituting the value of h2 (3h1) into the equation:
Ratio of Surface Areas = h1 / (3h1) = 1 / 3
Therefore, the ratio of the surface areas for this pair of similar cylinders is 1:3.