Question

1. find the surface area of a cylinder - shaped water reservoir. assuming the radius is 10 in and the height is 3 in. use 3.14 for π.

a. 628 in²
b. 188.4 in²
c. 816.4 in²
d. 200 in²

Explanation:

Step1: Recall the formula for the surface area of a cylinder

The surface area \( S \) of a cylinder is given by the formula \( S = 2\pi r^2+ 2\pi rh \), where \( r \) is the radius and \( h \) is the height.

Step2: Substitute the given values into the formula

We are given that \( r = 10 \) in, \( h = 3 \) in, and \( \pi = 3.14 \).

First, calculate the area of the two circular bases (\( 2\pi r^2 \)):
\[
2\times3.14\times10^2=2\times3.14\times100 = 628
\]

Next, calculate the lateral (curved) surface area (\( 2\pi rh \)):
\[
2\times3.14\times10\times3= 188.4
\]

Step3: Add the two areas together to get the total surface area

\[
S=628 + 188.4=816.4
\]

Answer:

c. \( 816.4\ \text{in}^2 \)