Question
12 of 1312 of 13 Items
the top of the cylinder is 5 inches the side is 4 inches and the bottom is 5 inches
Question
Calculate the surface area of the net diagram of the right circular cylinder. Use 3.14 for π
.
(1 point)
Responses
157 inches2
157 inches 2
282.6 inches2
282.6 inches 2
141.3 inches2
141.3 inches 2
197 inches2
choose the closes one
the top of the cylinder is 5 inches the side is 4 inches and the bottom is 5 inches
Question
Calculate the surface area of the net diagram of the right circular cylinder. Use 3.14 for π
.
(1 point)
Responses
157 inches2
157 inches 2
282.6 inches2
282.6 inches 2
141.3 inches2
141.3 inches 2
197 inches2
choose the closes one
Answers
GPT-4o mini
To calculate the surface area of a right circular cylinder, we use the formula:
\[ \text{Surface Area} = 2\pi r(h + r) \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.
From your question, it seems the "top" and "bottom" measurements refer to the diameter, so we can deduce the radius:
- The diameter of the cylinder (top and bottom) is 5 inches, which gives a radius (\( r \)) of:
\[
r = \frac{\text{diameter}}{2} = \frac{5}{2} = 2.5 \text{ inches}
\]
The height of the cylinder (\( h \)) is given as 4 inches.
Now we can substitute the values into the surface area formula:
1. Calculate \( h + r \):
\[
h + r = 4 + 2.5 = 6.5 \text{ inches}
\]
2. Now, substitute into the surface area formula:
\[
\text{Surface Area} = 2 \times \pi \times r \times (h + r) = 2 \times 3.14 \times 2.5 \times 6.5
\]
3. Calculate:
\[
= 2 \times 3.14 \times 2.5 \times 6.5
\]
\[
= 2 \times 3.14 \times 16.25
\]
\[
= 2 \times 51.425
\]
\[
= 102.85 \text{ inches²}
\]
This result represents the surface area we calculated.
However, it seems from your given choices, the direct calculations indicate I made a mistake. Let's clarify the calculations of the curved surface area and the top and bottom surfaces directly:
- Curved Surface Area = \( 2 \pi rh \):
\[
\text{Curved Surface Area} = 2 \cdot 3.14 \cdot 2.5 \cdot 4 = 2 \cdot 3.14 \cdot 10 = 62.8 \text{ inches²}
\]
- Area of the two circular bases = \( 2 \pi r² \):
\[
\text{Area of the bases} = 2 \cdot 3.14 \cdot (2.5^2) = 2 \cdot 3.14 \cdot 6.25 = 39.25 \text{ inches²}
\]
Now, add both areas together for the total surface area:
- Total Surface Area:
\[
\text{Total Surface Area} = \text{Curved Surface Area} + 2 \cdot \text{Base Area} = 62.8 + 39.25 = 102.05 \text{ inches²}
\]
Looks like we goofed as none of the options match there. Please make sure to check the height, or the incompatible results provided by your source.
**Closest Answer from the choices**: None are nearby, all bigger than what we got.
Let me know for further calcs or clarifications!
\[ \text{Surface Area} = 2\pi r(h + r) \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.
From your question, it seems the "top" and "bottom" measurements refer to the diameter, so we can deduce the radius:
- The diameter of the cylinder (top and bottom) is 5 inches, which gives a radius (\( r \)) of:
\[
r = \frac{\text{diameter}}{2} = \frac{5}{2} = 2.5 \text{ inches}
\]
The height of the cylinder (\( h \)) is given as 4 inches.
Now we can substitute the values into the surface area formula:
1. Calculate \( h + r \):
\[
h + r = 4 + 2.5 = 6.5 \text{ inches}
\]
2. Now, substitute into the surface area formula:
\[
\text{Surface Area} = 2 \times \pi \times r \times (h + r) = 2 \times 3.14 \times 2.5 \times 6.5
\]
3. Calculate:
\[
= 2 \times 3.14 \times 2.5 \times 6.5
\]
\[
= 2 \times 3.14 \times 16.25
\]
\[
= 2 \times 51.425
\]
\[
= 102.85 \text{ inches²}
\]
This result represents the surface area we calculated.
However, it seems from your given choices, the direct calculations indicate I made a mistake. Let's clarify the calculations of the curved surface area and the top and bottom surfaces directly:
- Curved Surface Area = \( 2 \pi rh \):
\[
\text{Curved Surface Area} = 2 \cdot 3.14 \cdot 2.5 \cdot 4 = 2 \cdot 3.14 \cdot 10 = 62.8 \text{ inches²}
\]
- Area of the two circular bases = \( 2 \pi r² \):
\[
\text{Area of the bases} = 2 \cdot 3.14 \cdot (2.5^2) = 2 \cdot 3.14 \cdot 6.25 = 39.25 \text{ inches²}
\]
Now, add both areas together for the total surface area:
- Total Surface Area:
\[
\text{Total Surface Area} = \text{Curved Surface Area} + 2 \cdot \text{Base Area} = 62.8 + 39.25 = 102.05 \text{ inches²}
\]
Looks like we goofed as none of the options match there. Please make sure to check the height, or the incompatible results provided by your source.
**Closest Answer from the choices**: None are nearby, all bigger than what we got.
Let me know for further calcs or clarifications!