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Anjali needs to paint the outside of an entire coffee can for an art class project. Given the figure below, calculate the can’s...Question
Anjali needs to paint the outside of an entire coffee can for an art class project.
Given the figure below, calculate the can’s surface area to help her determine how much paint she will need.
Use 3.14 for pi (𝜋).
Formula for surface area of a cylinder: SA = 2𝜋r 2
+ 2𝜋rℎ
(1 point)
Responses
56.52 in2
56.52 in2
117.75 in2
117.75 in2
174.27 in2
174.27 in2
197,34 in2
Given the figure below, calculate the can’s surface area to help her determine how much paint she will need.
Use 3.14 for pi (𝜋).
Formula for surface area of a cylinder: SA = 2𝜋r 2
+ 2𝜋rℎ
(1 point)
Responses
56.52 in2
56.52 in2
117.75 in2
117.75 in2
174.27 in2
174.27 in2
197,34 in2
Answers
GPT-4o mini
To calculate the surface area (SA) of a cylinder, we can use the formula:
\[ SA = 2\pi r^2 + 2\pi rh \]
Where:
- \( r \) is the radius of the base of the cylinder
- \( h \) is the height of the cylinder
- \( \pi \) is given as 3.14
Since the specific values for the radius \( r \) and height \( h \) of the coffee can have not been provided, let’s consider an example to demonstrate how to calculate it.
Suppose, for example, the radius \( r \) is 3 inches and the height \( h \) is 5 inches.
1. Calculate the area of the two circular bases:
\[ 2\pi r^2 = 2 \times 3.14 \times (3)^2 \]
\[ = 2 \times 3.14 \times 9 \]
\[ = 56.52 \, \text{in}^2 \]
2. Calculate the lateral surface area:
\[ 2\pi rh = 2 \times 3.14 \times 3 \times 5 \]
\[ = 2 \times 3.14 \times 15 \]
\[ = 94.2 \, \text{in}^2 \]
3. Add both areas together:
\[ SA = 56.52 + 94.2 = 150.72 \, \text{in}^2 \]
Now, without the dimensions, we cannot determine which of the available options (56.52 in², 117.75 in², 174.27 in², 197.34 in²) is correct. If you provide the radius and height of the coffee can, I can calculate the exact surface area.
\[ SA = 2\pi r^2 + 2\pi rh \]
Where:
- \( r \) is the radius of the base of the cylinder
- \( h \) is the height of the cylinder
- \( \pi \) is given as 3.14
Since the specific values for the radius \( r \) and height \( h \) of the coffee can have not been provided, let’s consider an example to demonstrate how to calculate it.
Suppose, for example, the radius \( r \) is 3 inches and the height \( h \) is 5 inches.
1. Calculate the area of the two circular bases:
\[ 2\pi r^2 = 2 \times 3.14 \times (3)^2 \]
\[ = 2 \times 3.14 \times 9 \]
\[ = 56.52 \, \text{in}^2 \]
2. Calculate the lateral surface area:
\[ 2\pi rh = 2 \times 3.14 \times 3 \times 5 \]
\[ = 2 \times 3.14 \times 15 \]
\[ = 94.2 \, \text{in}^2 \]
3. Add both areas together:
\[ SA = 56.52 + 94.2 = 150.72 \, \text{in}^2 \]
Now, without the dimensions, we cannot determine which of the available options (56.52 in², 117.75 in², 174.27 in², 197.34 in²) is correct. If you provide the radius and height of the coffee can, I can calculate the exact surface area.