Question

calculate the surface area of the following. round each answer to the nearest tenth. 7.7 mi 15.8 mi

Explanation:

Step1: Identify radius and height

The radius $r = \frac{7.7}{2}=3.85$ mi and height $h = 15.8$ mi.

Step2: Calculate area of two - bases

The area of a circle is $A_{base}=\pi r^{2}$. The area of two bases is $A_{2 - bases}=2\pi r^{2}=2\pi(3.85)^{2}$.
$A_{2 - bases}=2\pi\times14.8225\approx2\times3.14\times14.8225 = 93.0427$ mi².

Step3: Calculate lateral - surface area

The lateral - surface area of a cylinder is $A_{lateral}=2\pi r h$.
$A_{lateral}=2\pi\times3.85\times15.8=2\times3.14\times3.85\times15.8 = 381.7772$ mi².

Step4: Calculate total surface area

The total surface area $A = A_{2 - bases}+A_{lateral}$.
$A=93.0427 + 381.7772=474.8199\approx474.8$ mi².

Answer:

$474.8$ mi²