Question

what is the surface area of this cylinder? round your answer to the nearest hundredth. 14 cm 7.8 cm square centimeters

Explanation:

Step1: Identify radius and height

The radius $r = 14\div2= 7$ cm and height $h = 7.8$ cm.

Step2: Calculate area of two - bases

The area of a circle is $A_{base}=\pi r^{2}$. For two bases, $A_{2bases}=2\pi r^{2}=2\times\pi\times7^{2}=2\times\pi\times49 = 98\pi$ $cm^{2}$.

Step3: Calculate lateral - surface area

The lateral - surface area of a cylinder is $A_{lateral}=2\pi r h$. Substitute $r = 7$ cm and $h = 7.8$ cm, we get $A_{lateral}=2\times\pi\times7\times7.8=109.2\pi$ $cm^{2}$.

Step4: Calculate total surface area

The total surface area $A = A_{2bases}+A_{lateral}=98\pi + 109.2\pi=207.2\pi$ $cm^{2}$.
Now, substitute $\pi\approx3.14159$: $A\approx207.2\times3.14159 = 649.937448\approx649.94$ $cm^{2}$.

Answer:

$649.94$