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

Explanation:

Step1: Recall surface - area formula

The surface - area formula of a cylinder is $S = 2\pi r^2+2\pi rh$, where $r$ is the radius and $h$ is the height. Given $r = 10$ in and $h = 17$ in.

Step2: Calculate the area of the two bases

The area of one base is $A_{base}=\pi r^2$. For two bases, $A_{2bases}=2\pi r^2$. Substitute $r = 10$ in, we get $A_{2bases}=2\times3.14\times10^2=2\times3.14\times100 = 628$ square inches.

Step3: Calculate the lateral - surface area

The lateral - surface area formula is $A_{lateral}=2\pi rh$. Substitute $r = 10$ in and $h = 17$ in, we get $A_{lateral}=2\times3.14\times10\times17= 2\times3.14\times170=1067.6$ square inches.

Step4: Calculate the total surface area

$S=A_{2bases}+A_{lateral}$. So $S = 628+1067.6=1695.6$ square inches.

Answer:

$1695.6$