Question
What is the surface area of this cylinder? The radius is 3.2 in and the height is 2.3 in Surface area = Atop + Abottom + Aside Use 𝜋 ≈ 3.14 and round your answer to the nearest hundredth. Find the radius and height of the cylinder. The circle on the bottom of the cylinder is the same, so: Find the circumference of the top circle. Now find the area of the curved surface. The curved surface is a rectangle. One side length is the height, and the other side length is the circumference of the circle. Now add the areas to find the surface area of the cylinder. The surface area of the cylinder is about _____ square inches
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the surface area of the cylinder, we can use the formula:
\[
\text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}}
\]
Where:
- \( A_{\text{top}} \) and \( A_{\text{bottom}} \) are the areas of the circular top and bottom, respectively.
- \( A_{\text{side}} \) is the area of the curved surface of the cylinder.
### Step 1: Calculate the Area of the Top and Bottom Circles
The area \( A \) of a circle is given by the formula:
\[
A = \pi r^2
\]
Where:
- \( r \) is the radius.
Given \( r = 3.2 \) inches:
\[
A_{\text{top}} = A_{\text{bottom}} = \pi (3.2)^2
\]
Calculating:
\[
A_{\text{top}} = A_{\text{bottom}} = 3.14 \times (3.2)^2 = 3.14 \times 10.24 \approx 32.24 \, \text{square inches}
\]
Since we have two identical circles:
\[
A_{\text{top}} + A_{\text{bottom}} = 32.24 + 32.24 = 64.48 \, \text{square inches}
\]
### Step 2: Calculate the Circumference of the Top Circle
The circumference \( C \) of a circle is given by:
\[
C = 2\pi r
\]
Calculating:
\[
C = 2 \times 3.14 \times 3.2 \approx 19.88 \, \text{inches}
\]
### Step 3: Calculate the Area of the Curved Surface
The area of the curved surface \( A_{\text{side}} \) can be viewed as a rectangle with one side being the height \( h \) and the other side being the circumference \( C \):
\[
A_{\text{side}} = C \times h
\]
Given \( h = 2.3 \) inches:
\[
A_{\text{side}} = 19.88 \times 2.3 \approx 45.70 \, \text{square inches}
\]
### Step 4: Calculate the Total Surface Area
Now, add the areas together to find the total surface area of the cylinder:
\[
\text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}} = 64.48 + 45.70 \approx 110.18 \, \text{square inches}
\]
### Final Answer
The surface area of the cylinder is approximately \( \boxed{110.18} \) square inches.
\[
\text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}}
\]
Where:
- \( A_{\text{top}} \) and \( A_{\text{bottom}} \) are the areas of the circular top and bottom, respectively.
- \( A_{\text{side}} \) is the area of the curved surface of the cylinder.
### Step 1: Calculate the Area of the Top and Bottom Circles
The area \( A \) of a circle is given by the formula:
\[
A = \pi r^2
\]
Where:
- \( r \) is the radius.
Given \( r = 3.2 \) inches:
\[
A_{\text{top}} = A_{\text{bottom}} = \pi (3.2)^2
\]
Calculating:
\[
A_{\text{top}} = A_{\text{bottom}} = 3.14 \times (3.2)^2 = 3.14 \times 10.24 \approx 32.24 \, \text{square inches}
\]
Since we have two identical circles:
\[
A_{\text{top}} + A_{\text{bottom}} = 32.24 + 32.24 = 64.48 \, \text{square inches}
\]
### Step 2: Calculate the Circumference of the Top Circle
The circumference \( C \) of a circle is given by:
\[
C = 2\pi r
\]
Calculating:
\[
C = 2 \times 3.14 \times 3.2 \approx 19.88 \, \text{inches}
\]
### Step 3: Calculate the Area of the Curved Surface
The area of the curved surface \( A_{\text{side}} \) can be viewed as a rectangle with one side being the height \( h \) and the other side being the circumference \( C \):
\[
A_{\text{side}} = C \times h
\]
Given \( h = 2.3 \) inches:
\[
A_{\text{side}} = 19.88 \times 2.3 \approx 45.70 \, \text{square inches}
\]
### Step 4: Calculate the Total Surface Area
Now, add the areas together to find the total surface area of the cylinder:
\[
\text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}} = 64.48 + 45.70 \approx 110.18 \, \text{square inches}
\]
### Final Answer
The surface area of the cylinder is approximately \( \boxed{110.18} \) square inches.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.