Find the surface area of the cylinder. Use the approximation of 3.14 for pi. The diameter is 2 yd. height is 3 yd.

Answer 1

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.

Answer 2

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

Answer 3

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.