Question
Find the surface area of the cylinder. Use the approximation of 3.14 for pi. The diameter is 2 yd. height is 3 yd.
Answers
GPT-4o mini
To find the surface area of a cylinder, we use the formula:
\[
\text{Surface Area} = 2\pi r(h + r)
\]
where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder.
First, we need to find the radius. The diameter of the cylinder is given as 2 yards, so:
\[
r = \frac{\text{diameter}}{2} = \frac{2 \, \text{yd}}{2} = 1 \, \text{yd}
\]
Now we can plug in the values into the surface area formula. The height \( h \) is given as 3 yards. Using \( \pi \approx 3.14 \):
\[
\text{Surface Area} = 2 \times 3.14 \times 1 \, \text{yd} \times (3 \, \text{yd} + 1 \, \text{yd})
\]
Calculating the expression inside the parentheses:
\[
h + r = 3 \, \text{yd} + 1 \, \text{yd} = 4 \, \text{yd}
\]
Now substitute this back into the formula:
\[
\text{Surface Area} = 2 \times 3.14 \times 1 \, \text{yd} \times 4 \, \text{yd}
\]
Now calculate the surface area:
\[
\text{Surface Area} = 2 \times 3.14 \times 4 \, \text{yd}^2
\]
Calculating:
\[
2 \times 3.14 = 6.28
\]
\[
6.28 \times 4 = 25.12
\]
Thus, the surface area of the cylinder is:
\[
\text{Surface Area} \approx 25.12 \, \text{yd}^2
\]
So the surface area of the cylinder is approximately **25.12 square yards**.
\[
\text{Surface Area} = 2\pi r(h + r)
\]
where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder.
First, we need to find the radius. The diameter of the cylinder is given as 2 yards, so:
\[
r = \frac{\text{diameter}}{2} = \frac{2 \, \text{yd}}{2} = 1 \, \text{yd}
\]
Now we can plug in the values into the surface area formula. The height \( h \) is given as 3 yards. Using \( \pi \approx 3.14 \):
\[
\text{Surface Area} = 2 \times 3.14 \times 1 \, \text{yd} \times (3 \, \text{yd} + 1 \, \text{yd})
\]
Calculating the expression inside the parentheses:
\[
h + r = 3 \, \text{yd} + 1 \, \text{yd} = 4 \, \text{yd}
\]
Now substitute this back into the formula:
\[
\text{Surface Area} = 2 \times 3.14 \times 1 \, \text{yd} \times 4 \, \text{yd}
\]
Now calculate the surface area:
\[
\text{Surface Area} = 2 \times 3.14 \times 4 \, \text{yd}^2
\]
Calculating:
\[
2 \times 3.14 = 6.28
\]
\[
6.28 \times 4 = 25.12
\]
Thus, the surface area of the cylinder is:
\[
\text{Surface Area} \approx 25.12 \, \text{yd}^2
\]
So the surface area of the cylinder is approximately **25.12 square yards**.
What is the diameter is 6 inches and height of 4 inches how much square inches of paper will be needed to label the OUTSIDE of the can
GPT-4o mini
To find the surface area of a cylinder so that we can determine how much paper is needed to label the outside, we will use the same surface area formula:
\[
\text{Surface Area} = 2\pi r(h + r)
\]
where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder.
**Step 1: Find the radius.**
The diameter of the cylinder is given as 6 inches, so:
\[
r = \frac{\text{diameter}}{2} = \frac{6 \, \text{in}}{2} = 3 \, \text{in}
\]
**Step 2: Use the height.**
The height \( h \) is given as 4 inches.
**Step 3: Substitute the values into the surface area formula.**
Using \( \pi \approx 3.14 \):
\[
\text{Surface Area} = 2 \times 3.14 \times 3 \, \text{in} \times (4 \, \text{in} + 3 \, \text{in})
\]
Calculating the expression inside the parentheses:
\[
h + r = 4 \, \text{in} + 3 \, \text{in} = 7 \, \text{in}
\]
Now substitute this back into the formula:
\[
\text{Surface Area} = 2 \times 3.14 \times 3 \, \text{in} \times 7 \, \text{in}
\]
**Step 4: Calculate the surface area.**
First, calculate \( 2 \times 3.14 \):
\[
2 \times 3.14 = 6.28
\]
Next, multiply by \( 3 \, \text{in} \):
\[
6.28 \times 3 \, \text{in} = 18.84
\]
Now, multiply by \( 7 \, \text{in} \):
\[
18.84 \times 7 \, \text{in} = 131.88
\]
Thus, the surface area of the cylinder (the amount of paper needed to label the outside) is approximately:
\[
\text{Surface Area} \approx 131.88 \, \text{in}^2
\]
So, you will need approximately **131.88 square inches** of paper to label the outside of the can.
\[
\text{Surface Area} = 2\pi r(h + r)
\]
where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder.
**Step 1: Find the radius.**
The diameter of the cylinder is given as 6 inches, so:
\[
r = \frac{\text{diameter}}{2} = \frac{6 \, \text{in}}{2} = 3 \, \text{in}
\]
**Step 2: Use the height.**
The height \( h \) is given as 4 inches.
**Step 3: Substitute the values into the surface area formula.**
Using \( \pi \approx 3.14 \):
\[
\text{Surface Area} = 2 \times 3.14 \times 3 \, \text{in} \times (4 \, \text{in} + 3 \, \text{in})
\]
Calculating the expression inside the parentheses:
\[
h + r = 4 \, \text{in} + 3 \, \text{in} = 7 \, \text{in}
\]
Now substitute this back into the formula:
\[
\text{Surface Area} = 2 \times 3.14 \times 3 \, \text{in} \times 7 \, \text{in}
\]
**Step 4: Calculate the surface area.**
First, calculate \( 2 \times 3.14 \):
\[
2 \times 3.14 = 6.28
\]
Next, multiply by \( 3 \, \text{in} \):
\[
6.28 \times 3 \, \text{in} = 18.84
\]
Now, multiply by \( 7 \, \text{in} \):
\[
18.84 \times 7 \, \text{in} = 131.88
\]
Thus, the surface area of the cylinder (the amount of paper needed to label the outside) is approximately:
\[
\text{Surface Area} \approx 131.88 \, \text{in}^2
\]
So, you will need approximately **131.88 square inches** of paper to label the outside of the can.