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 $\boldsymbol{square}$ square millimeters

Explanation:

Step1: Identify correct net

The cylinder has diameter $d=20$ mm, so circumference $C=\pi d=20\pi$ mm. The rectangle in the net must match this length. The top diagram has a rectangle of length $20\pi$ mm, so this is the correct net.

Step2: Calculate radius of cylinder

Radius $r = \frac{d}{2} = \frac{20}{2} = 10$ mm

Step3: Calculate area of two circles

Area of one circle: $\pi r^2 = \pi (10)^2 = 100\pi$ mm². For two circles: $2\times100\pi = 200\pi$ mm²

Step4: Calculate lateral surface area

Lateral area = $C\times h = 20\pi\times7 = 140\pi$ mm²

Step5: Total surface area

Add the two areas: $200\pi + 140\pi = 340\pi$ mm²

Step6: Convert to decimal

$340\pi \approx 340\times3.14159265 \approx 1068.1$ mm²

Answer:

1. Correct net: The top diagram (with rectangle length $20\pi$ mm)
2. Surface area: about $\boldsymbol{1068.1}$ square millimeters