A right cylinder has a radius of 6 m and a surface area of 84 m². Find the surface area of a similar cylinder with a radius of 2 m

A=2πrh+2πr2

84 = 2π6h + 2π36
Solve for h, then do similar equation to solve for radius = 2

To find the surface area of a similar cylinder with a radius of 2 m, we can use the concept of similar shapes. Since the two cylinders are similar, their corresponding sides are proportional.

The surface area of a cylinder is given by the formula:

Surface Area = 2πr(r + h)

Given that the radius of the original cylinder is 6 m and the surface area is 84 m², we can substitute these values into the formula:

84 = 2π(6)(6 + h)

Now, let's solve for h:

84 = 72π + 2πh
84 - 72π = 2πh
h = (84 - 72π) / (2π)
h ≈ 2.121 m

Now that we have the height of the original cylinder (h ≈ 2.121 m), we can calculate the height of the similar cylinder using the concept of proportions.

Since the ratio of the original radius to the similar radius is 6:2 (or 3:1), the ratio of the original height to the similar height will also be 3:1.

So, the height of the similar cylinder is (2.121 m)/3 ≈ 0.707 m.

Now we can find the surface area of the similar cylinder using the formula:

Surface Area = 2πr(r + h)

Substituting the values, we get:

Surface Area = 2π(2)(2 + 0.707)
Surface Area = 2π(2)(2.707)
Surface Area ≈ 34 m²

Therefore, the surface area of the similar cylinder with a radius of 2 m is approximately 34 m².

To find the surface area of a similar cylinder, we need to know the relationship between the surface areas of similar shapes. The surface area of a cylinder is directly proportional to the square of its radius.

Let's call the surface area of the first cylinder SA1 and the surface area of the second cylinder SA2. The ratio of the surface areas of similar cylinders is the square of the ratio of their radii.

In this case, the ratio of the radii is 2 m / 6 m = 1/3. So, the ratio of the surface areas is (1/3)² = 1/9.

Now, we can set up the following equation to find the surface area of the second cylinder:

SA2 = (1/9) * SA1

Substituting the given surface area of the first cylinder (SA1 = 84 m²):

SA2 = (1/9) * 84 m²
SA2 = 9.33 m²

Therefore, the surface area of the second cylinder with a radius of 2 m is 9.33 m².