Question

1. check for reasonableness is $250\\ \text{cm}^2$ a reasonable answer for the surface area of the cylinder represented by the net? explain.

3 cm
20 cm

Explanation:

Step1: Identify cylinder dimensions

Diameter $d=20$ cm, so radius $r=\frac{20}{2}=10$ cm; height $h=3$ cm.

Step2: Calculate area of two circles

Formula: $2\times\pi r^2$
$\text{Area} = 2\times\pi\times10^2 = 200\pi \approx 628.32$ cm²

Step3: Calculate lateral surface area

Formula: $2\pi r h$
$\text{Area} = 2\times\pi\times10\times3 = 60\pi \approx 188.50$ cm²

Step4: Total surface area

Sum the two results: $628.32 + 188.50 = 816.82$ cm²

Step5: Compare to 250 cm²

The actual surface area is ~816.82 cm², far larger than 250 cm².

Answer:

No, 250 cm² is not a reasonable answer. The actual total surface area of the cylinder is approximately 816.82 cm², which is much larger than 250 cm².