We want to determine which of the given cylindrical containers has the greatest surface area. To do so, we will find the surface area of each container and compare the results.
Container I
Let's consider the first container.
We can see that this container is the cylinder with a radius of 5.2 centimeters and a height of 12 centimeters. To calculate the surface area of the cylinder, we will use the following formula.
S=2π rh+2π r^2
In this formula, r is the radius of the base and h is the height of the cylinder. We can substitute the radius and the height of the given container into the formula. Then we will simplify the right-hand side to get the surface area.
Therefore, the surface area of the first container is about 562.0 square centimeters.
Container II
Now let's take a look at Container II.
This container is the cylinder with a radius of 8 centimeters and a height of 5 centimeters. Using the formula for the surface area of a cylinder, we can calculate the surface area of Container II.
We got that the surface area of Container II is about 653.5 square centimeters.
Container III
Next, we will consider Container III.
Container III is the cylinder with a radius of 5.7 centimeters and a height of 10 centimeters. Similar as before, we will find the surface area of the container using the formula for the surface area of a cylinder.
Therefore, the surface area of Container III is about 562.3 square centimeters.
Container IV
Finally, we will analyze Container IV.
Container IV is the cylinder with a diameter of 5.4 centimeters and a height of 11 centimeters. We will find the radius of the container by dividing the diameter by 2.
Therefore, the radius is equal to 2.7 centimeters. Now, we can use the formula for the surface area of a cylinder to calculate the surface area of Container IV.
