What is the surface area of this cylinder?

Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth. r=16ft h=4ft

1 answer

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

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

where:

  • \( r \) is the radius of the base,
  • \( h \) is the height of the cylinder.

Given:

  • \( r = 16 , \text{ft} \)
  • \( h = 4 , \text{ft} \)
  • Use \( \pi \approx 3.14 \)

Now, let's calculate each part of the formula.

  1. Calculate the area of the two circular bases: \[ 2\pi r^2 = 2 \times 3.14 \times (16)^2 \] \[ = 2 \times 3.14 \times 256 \] \[ = 6.28 \times 256 \] \[ = 1609.28 , \text{ft}^2 \]

  2. Calculate the area of the curved surface: \[ 2\pi rh = 2 \times 3.14 \times 16 \times 4 \] \[ = 2 \times 3.14 \times 64 \] \[ = 6.28 \times 64 \] \[ = 401.92 , \text{ft}^2 \]

  3. Now add the two areas together to find the total surface area: \[ \text{Surface Area} = 1609.28 + 401.92 = 2011.20 , \text{ft}^2 \]

Therefore, the surface area of the cylinder, rounded to the nearest hundredth, is:

\[ \boxed{2011.20 , \text{ft}^2} \]