To calculate the lateral area, we must know that the lateral area of a right cylinder is the product of the circumference of the base and the height of the cylinder.
Note that the base is congruent to the top face. Therefore, their circumferences are the same.
L=2π rh
In this formula, r is the radius of the base and h is the height of the cylinder. In the given diagram, we can see that the radius r is equal to 16.5 meters and that the height h is equal to 16.5 meters. If we substitute these values in the formula, we can obtain the lateral area of the given cylinder.
The lateral area of the cylinder is about 1710.6m^2.
Surface area
To calculate the surface area of a cylinder, we can use the following formula.
S=L+2π r^2
In this formula, L is the lateral area of the cylinder and r is the radius of the base. Now, we can substitute L with 1710.6 and r with 16.5 into the formula for S. Let's do it!
The surface area of the cylinder is about 3421.2 m^2.
Alternative Solution
Alternative Solution
Notice that for the given cylinder, the radius r is equal to the height h. Therefore, the formula for the lateral area can be simplified. L=2 π rh
⇔ L=2 π r^2
Now, we can simplify the formula for the surface area.
&S=L+2π r^2 and L=2 π r^2 & [0.2em]
&⇕& [0.2em]
&S=L+L& [0.15em]
&S=2L&
