Determine the surface area of a cone if the radius of the base is 8 in. and the slant height of the cone is 10 in. Use π=3.14 and round your answer to the nearest hundredth.(1 point)

in.2

1 answer

To calculate the surface area of a cone, you can use the formula:

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

where:

  • \( r \) is the radius of the base,
  • \( l \) is the slant height.

Given:

  • \( r = 8 \) inches,
  • \( l = 10 \) inches,
  • \( \pi \approx 3.14 \).

Now, let's plug in the values into the formula.

  1. Calculate the area of the base: \[ \pi r^2 = 3.14 \times (8^2) = 3.14 \times 64 = 200.96 \text{ in}^2 \]

  2. Calculate the lateral surface area: \[ \pi r l = 3.14 \times 8 \times 10 = 3.14 \times 80 = 251.2 \text{ in}^2 \]

  3. Total surface area: \[ \text{Surface Area} = 200.96 + 251.2 = 452.16 \text{ in}^2 \]

Rounding to the nearest hundredth, the surface area of the cone is:

\[ \boxed{452.16} \text{ in}^2 \]