Question

a cylinder is shown below.which diagram is a net for the cylinder?what is the surface area of the cylinder?write your answer as a decimal rounded to the nearest tenth.about ____ square millimeters

Explanation:

Step1: Identify correct net

The net of a cylinder has a rectangle whose length equals the circumference of the circular base. The circumference of a circle is $C=2\pi r$. For $r=9$ mm, $C=2\pi(9)=18\pi$ mm. So the net with the $18\pi$ mm long rectangle is correct.

Step2: Recall surface area formula

Total surface area of a cylinder: $SA=2\pi r^2 + 2\pi r h$, where $r=9$ mm, $h=7$ mm.

Step3: Calculate area of two bases

Compute $2\pi r^2$:
$2\pi (9)^2 = 2\pi(81)=162\pi$

Step4: Calculate lateral surface area

Compute $2\pi r h$:
$2\pi(9)(7)=126\pi$

Step5: Sum the areas

Total surface area:
$SA=162\pi + 126\pi=288\pi$

Step6: Convert to decimal approximation

Use $\pi\approx3.14159$:
$288\times3.14159\approx904.78$

Answer:

1. Correct net: The diagram with the rectangle labeled $18\pi$ mm and 7 mm, paired with two 9 mm radius circles.
2. Surface area: about $904.8$ square millimeters