Find the surface area of the cylinder. Use the approximation 3.14 for pi.

height is 8
diameter is 7

1 answer

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

\[ \text{Surface Area} = 2\pi r(h + r) \]

where \( r \) is the radius, \( h \) is the height, and \( \pi \) can be approximated as 3.14.

Given:

  • Height \( h = 8 \)
  • Diameter = 7, so the radius \( r = \frac{7}{2} = 3.5 \)

Now, substitute the values into the formula:

  1. Calculate \( r \) and \( h \):

    • \( r = 3.5 \)
    • \( h = 8 \)
  2. Substitute into the surface area formula:

\[ \text{Surface Area} = 2 \times 3.14 \times 3.5 \times (8 + 3.5) \]

  1. Calculate \( (8 + 3.5) \):

\[ 8 + 3.5 = 11.5 \]

  1. Now plug this back into the equation:

\[ \text{Surface Area} = 2 \times 3.14 \times 3.5 \times 11.5 \]

  1. Calculate step by step:
    • First, calculate \( 2 \times 3.14 = 6.28 \)
    • Then, \( 6.28 \times 3.5 = 21.98 \)
    • Finally, \( 21.98 \times 11.5 \)

\[ 21.98 \times 11.5 = 253.77 \]

Thus, the surface area of the cylinder is approximately:

\[ \text{Surface Area} \approx 253.77 \]

So, the surface area of the cylinder is approximately 253.77 square units.