To find the surface area of a cone, we can use the formula for the surface area \( A \), which is given by:
\[ A = \pi r^2 + \pi r l \]
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 14 inches, so the radius \( r \) is half of that:
\[ r = \frac{14}{2} = 7 \text{ inches} \]
- The slant height \( l \) is given as 20 inches.
Now, we can substitute \( r \) and \( l \) into the surface area formula:
- Calculate the base area:
\[ \pi r^2 = \pi (7)^2 = \pi \times 49 \]
- Calculate the lateral surface area:
\[ \pi r l = \pi (7)(20) = 140\pi \]
Now, combine both parts to find the total surface area:
\[ A = \pi \times 49 + 140\pi = 49\pi + 140\pi = 189\pi \]
Now, we can approximate \( \pi \) as 3.14 for calculation:
\[ A \approx 189 \times 3.14 \approx 592.26 \text{ square inches} \]
Thus, the surface area of the cone to the nearest hundredth is:
\[ \boxed{592.26 \text{ square inches}} \]
1 answer