Question

a cylinder has a height of 7 feet and a diameter of 12 feet. which measurement is closest to the total surface area of the cylinder in square feet?
equation: $b = 2\pi r^2 + 2\pi r \square$
radius: $r = 6$
height: $h = 7$
final answer:

Explanation:

Step1: Recall the surface area formula for a cylinder

The formula for the total surface area \( B \) of a cylinder is \( B = 2\pi r^{2}+2\pi rh \), where \( r \) is the radius and \( h \) is the height. We know that the diameter is 12 feet, so the radius \( r=\frac{12}{2} = 6 \) feet (wait, the given radius in the problem's image is also 6, which matches), and the height \( h = 7 \) feet.

Step2: Substitute the values of \( r \) and \( h \) into the formula

Substitute \( r = 6 \) and \( h=7 \) into \( B = 2\pi r^{2}+2\pi rh \):
First, calculate \( 2\pi r^{2} \):
\( 2\pi(6)^{2}=2\pi\times36 = 72\pi \)
Then, calculate \( 2\pi rh \):
\( 2\pi\times6\times7=84\pi \)
Now, add these two results together:
\( B=72\pi + 84\pi=156\pi \)
If we use \( \pi\approx3.14 \), then \( B\approx156\times3.14 = 489.84 \) square feet.

Answer:

The total surface area of the cylinder is approximately \( \boldsymbol{490} \) square feet (or \( 156\pi\approx489.84 \), which is closest to 490).