what is the surface area of this cylinder? use $piapprox3.14$ and round your answer to the nearest…

Explanation:

Step1: Identify the formula for cylinder surface area

The formula for the surface area of a cylinder is $S = 2\pi r^2+ 2\pi rh$, where $r$ is the radius and $h$ is the height.

Step2: Determine the radius and height values

Given that the radius $r = 24$ m and height $h=9$ m.

Step3: Calculate the area of the two - circular bases

The area of one circular base is $A_{base}=\pi r^{2}$. For two bases, $A_{2bases}=2\pi r^{2}=2\times3.14\times24^{2}=2\times3.14\times576 = 3617.28$ square meters.

Step4: Calculate the lateral surface area

The lateral - surface area formula is $A_{lateral}=2\pi rh$. Substitute $r = 24$ m and $h = 9$ m, we get $A_{lateral}=2\times3.14\times24\times9=2\times3.14\times216 = 1356.48$ square meters.

Step5: Calculate the total surface area

$S=A_{2bases}+A_{lateral}=3617.28 + 1356.48=4973.76$ square meters.

Answer:

$4973.76$