A circular cone has a diameter of 8 in. and a slant height of 10 in. What is the surface area of the cone to the nearest inch?

(1 point)
O 63 in.?
• 452 in.?
• 176 in.?
302 in.?

1 answer

To find 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, and \( l \) is the slant height.

  1. Find the radius \( r \):

    • The diameter of the cone is 8 in., so the radius is: \[ r = \frac{8}{2} = 4 \text{ in.} \]
  2. Use the given slant height \( l \):

    • The slant height \( l \) is given as 10 in.
  3. Calculate the surface area:

    • Substitute \( r \) and \( l \) into the surface area formula: \[ \text{Surface Area} = \pi (4^2) + \pi (4)(10) \] \[ = \pi (16) + \pi (40) \] \[ = 16\pi + 40\pi \] \[ = 56\pi \]
  4. Calculate \( 56\pi \) using \( \pi \approx 3.14 \): \[ 56\pi \approx 56 \times 3.14 = 175.84 \text{ in}^2 \]

  5. Round to the nearest inch: \[ \approx 176 \text{ in}^2 \]

Therefore, the surface area of the cone is approximately 176 in².

The correct answer is 176 in².