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What is the surface area of this cylinder?

Use β€‹πœ‹ β‰ˆ 3.14 and round your answer to the nearest hundredth. r=9ft h=19ft

3 answers

To find the surface area of a cylinder, you can use the formula:

\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]

where:

  • \( r \) is the radius of the base of the cylinder,
  • \( h \) is the height of the cylinder,
  • \( \pi \) is a constant approximately equal to 3.14.

Given:

  • \( r = 9 \) ft
  • \( h = 19 \) ft

Now, substituting the given values into the formula:

  1. Calculate \( 2\pi r^2 \): \[ 2\pi r^2 = 2 \times 3.14 \times (9^2) = 2 \times 3.14 \times 81 \] \[ = 2 \times 3.14 \times 81 = 508.68 , \text{ft}^2 \]

  2. Calculate \( 2\pi rh \): \[ 2\pi rh = 2 \times 3.14 \times 9 \times 19 = 2 \times 3.14 \times 171 \] \[ = 2 \times 3.14 \times 171 = 1076.76 , \text{ft}^2 \]

  3. Now, add the two areas together to find the total surface area: \[ \text{Surface Area} = 508.68 + 1076.76 = 1585.44 , \text{ft}^2 \]

Rounding this to the nearest hundredth, the surface area of the cylinder is:

\[ \text{Surface Area} \approx 1585.44 , \text{ft}^2 \]

is this correct?

Let’s recheck each step of the calculation for the surface area of the cylinder using the given values: \( r = 9 \) ft and \( h = 19 \) ft, and \( \pi \approx 3.14 \).

The surface area \( A \) of a cylinder is calculated using the formula:

\[ A = 2\pi r^2 + 2\pi rh \]

Step 1: Calculate \( 2\pi r^2 \)

  1. Calculate \( r^2 \): \[ r^2 = 9^2 = 81 \]

  2. Then, calculate \( 2\pi r^2 \): \[ 2\pi r^2 = 2 \times 3.14 \times 81 = 2 \times 3.14 \times 81 = 508.68 , \text{ft}^2 \]

Step 2: Calculate \( 2\pi rh \)

  1. Calculate \( 2rh \): \[ 2rh = 2 \times 9 \times 19 = 2 \times 171 = 342 \]

  2. Then, calculate \( 2\pi rh \): \[ 2\pi rh = 3.14 \times 342 = 1076.28 , \text{ft}^2 \]

Step 3: Adding the two areas together

Now, add both surface areas:

\[ \text{Surface Area} = 508.68 + 1076.28 = 1584.96 , \text{ft}^2 \]

Conclusion

So, the correct total surface area of the cylinder, rounded to the nearest hundredth, is:

\[ \text{Surface Area} \approx 1584.96 , \text{ft}^2 \]

Thank you for prompting the check! So, the final answer is 1584.96 ftΒ².