Question

is this righ Cylinder Surface Area Problem

A cylindrical container has a diameter of 36 millimeters and a height of 18 millimeters. You need to find the total surface area of the container.

To solve this problem, use the formula for the surface area of a cylinder:

Surface Area
=
2
𝜋
𝑟
(
𝑟
+
ℎ
)
Where:

𝑟
is the radius of the cylinder

ℎ
is the height of the cylinder

Given:

Diameter = 36 mm, so the radius
𝑟
= 36 mm / 2 = 18 mm

Height
ℎ
= 18 mm

Using
𝜋
≈
3.14
:

Surface Area
=
2
×
3.14
×
18
×
(
18
+
18
)
Surface Area
=
2
×
3.14
×
18
×
36
Surface Area
=
2
×
3.14
×
648
Surface Area
=
4069.92
 square millimeters

Answer 1

no

Answer 2

Your approach to finding the total surface area of the cylindrical container is generally correct. However, there is a small error in your calculations. Let's go through the steps together to ensure accuracy.

1. **Identify the dimensions**:
- Diameter = 36 mm, so the radius \( r \) is:
\[
r = \frac{36 \text{ mm}}{2} = 18 \text{ mm}
\]
- Height \( h = 18 \text{ mm} \)

2. **Surface Area Formula**:
The formula for the total surface area \( S \) of a cylinder is:
\[
S = 2\pi r (r + h)
\]

3. **Plugging in the values**:
\[
S = 2 \times 3.14 \times 18 \times (18 + 18)
\]
Simplifying inside the parentheses:
\[
S = 2 \times 3.14 \times 18 \times 36
\]

4. **Calculating step by step**:
First, calculate \( 18 \times 36 \):
\[
18 \times 36 = 648
\]
Now plug this back into the expression:
\[
S = 2 \times 3.14 \times 648
\]
Calculate \( 2 \times 3.14 \):
\[
2 \times 3.14 = 6.28
\]
Now multiply by 648:
\[
S = 6.28 \times 648
\]
Performing the multiplication:
\[
S \approx 4074.24 \text{ square millimeters}
\]

5. **Final Result**:
The total surface area of the cylindrical container is approximately \( 4074.24 \, \text{mm}^2 \).

Your initial calculation of \( 4069.92 \) mm² was slightly off. The correct surface area, when calculated accurately, is approximately \( 4074.24 \) square millimeters.

Answer 3

Let’s go through the calculations again step by step to ensure we get the correct answer for the surface area of the cylindrical container.

### Given Parameters:
- **Diameter**: 36 mm
- **Radius \( r \)**:
\[
r = \frac{\text{Diameter}}{2} = \frac{36 \, \text{mm}}{2} = 18 \, \text{mm}
\]
- **Height \( h \)**:
\[
h = 18 \, \text{mm}
\]

### Surface Area Formula:
The surface area \( S \) of a cylinder is given by the formula:
\[
S = 2\pi r (r + h)
\]

### Plugging in the Values:
1. Substitute \( r \) and \( h \) into the formula:
\[
S = 2\pi \times 18 \times (18 + 18)
\]
This simplifies to:
\[
S = 2\pi \times 18 \times 36
\]

2. Calculate \( (r + h) \):
\[
r + h = 18 + 18 = 36
\]

3. Substitute back into the formula:
\[
S = 2\pi \times 18 \times 36
\]

### Calculate Step by Step:
1. Calculate \( 2 \times 18 = 36 \):
\[
S = 36\pi \times 36
\]
2. Now calculate \( 36 \times 36 = 1296 \):
\[
S = 1296\pi
\]
3. Using \( \pi \approx 3.14 \):
\[
S = 1296 \times 3.14 \approx 4071.84 \text{ mm}^2
\]

### Final Result:
Therefore, the total surface area of the cylindrical container is **approximately** \( 4071.84 \, \text{mm}^2 \).

If you believed the surface area calculation was incorrect or had further specifications, please clarify, and I’ll be happy to assist you!