Question

10 of 1210 of 12 Items



the top of the cylinder is 2cm and the round part is 5cm




Question
Find the surface area of a cylinder. Use 3.14 for π
.

Round your answer to the nearest tenths place.



(1 point)
Responses

87.9 cm2
87.9 cm 2

175.8 cm2
175.8 cm 2

120.3 cm2
120.3 cm 2

75.3 cm2

Answers

GPT-4o mini
To find the surface area of a cylinder, we can use the formula:

\[
SA = 2\pi r(h + r)
\]

Where:
- \(SA\) is the surface area,
- \(r\) is the radius of the base,
- \(h\) is the height of the cylinder,
- \(\pi\) is approximately 3.14.

From your question:
- The diameter of the top of the cylinder is given as 2 cm, which means the radius \(r\) is \( \frac{2}{2} = 1 \) cm.
- The height \(h\) of the cylinder is given as 5 cm.

Now we can substitute the values into the formula:

\[
SA = 2 \cdot 3.14 \cdot 1 \cdot (5 + 1)
\]

Calculating it step-by-step:

1. Calculate \(h + r\):
\[
h + r = 5 + 1 = 6
\]

2. Calculate \(2 \cdot 3.14 \cdot 1 \cdot 6\):
\[
SA = 2 \cdot 3.14 \cdot 6 = 2 \cdot 18.84 = 37.68
\]

3. Finally, round \(37.68\) to the nearest tenths place, which remains \(37.7\) cm².

This surface area doesn't match any options you provided. Let's check the calculations once more for any mistakes.

Using the surface area formula again:
- The cylinder has a top and bottom (2 circles), and the curved surface area.
- The correct formula for the total surface area of a cylinder is:

\[
SA = 2\pi r^2 + 2\pi rh
\]

Calculating the area again:
1. Area of the two circles:
\[
2\pi r^2 = 2 \cdot 3.14 \cdot (1)^2 = 2 \cdot 3.14 \cdot 1 = 6.28
\]

2. Area of the curved surface:
\[
2\pi rh = 2 \cdot 3.14 \cdot 1 \cdot 5 = 2 \cdot 3.14 \cdot 5 = 31.4
\]

Adding these two areas together:
\[
SA = 6.28 + 31.4 = 37.68
\]

Upon double-checking the calculations for potential misinterpretations or data entry errors, it seems the values used may not align perfectly with your options.

To clarify, it seems that there may be a miscommunication regarding either the dimensions or the selections you provided, which typically would lead to results around the \(37.68\) cm² area.

If we adjust cylinder parameters or if any details were omitted, please provide those for a reevaluation. I hope this clears up the surface area computation!

Related Questions