Question

find the surface area of the cylinder given the height and radius shown. note that the figure is not to scale.

Explanation:

Step1: Calculate the area of the two circular bases

The formula for the area of a circle is $A = \pi r^{2}$. Given $r = 7$, then the area of one base is $A_{base}=\pi\times7^{2}=49\pi$. The area of two bases is $A_{two - bases}=2\times49\pi = 98\pi$.

Step2: Calculate the lateral surface area

The formula for the lateral surface area of a cylinder is $A_{lateral}=2\pi r h$. Given $r = 7$ and $h = 15$, then $A_{lateral}=2\pi\times7\times15=210\pi$.

Step3: Calculate the total surface area

The total surface area of a cylinder $A = A_{two - bases}+A_{lateral}$. Substitute the values: $A=(98 + 210)\pi=308\pi$. Using $\pi\approx3.14$, we get $A = 308\times3.14=967.12$.

Answer:

$967.12$