what is the surface area of a cone with a diameter of 20 inches and a slant height of 25 inches? Eli wants enough material to cover his model castle roof. use 3.14 for pi, and round to the nearest hundredth.

- 1099
- 141.3
- 1256
- 1570
- 2616.67
- 523.33

1 answer

To find the surface area of a cone, we can use the formula:

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

where:

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

Given:

  • The diameter of the cone is 20 inches, so the radius \( r \) is \( \frac{20}{2} = 10 \) inches.
  • The slant height \( l \) is 25 inches.

Now, we can substitute the values into the formula.

  1. Calculate the area of the base: \[ \pi r^2 = 3.14 \times (10^2) = 3.14 \times 100 = 314 \]

  2. Calculate the lateral surface area: \[ \pi r l = 3.14 \times 10 \times 25 = 3.14 \times 250 = 785 \]

  3. Add the areas together to get the total surface area: \[ \text{Surface Area} = 314 + 785 = 1099 \]

Therefore, the surface area of the cone is 1099 square inches.

The answer is 1099.