A cone has diameter of 14 inches and slant height of 20 inches. Find the surface area to nearesth hundredth. Need units.
To find the surface area of a cone, we need to remember that it consists of two parts: the curved surface area and the base area.
The curved surface area, which is the lateral area of the cone, can be found using the formula:
\(\text{Curved Surface Area} = \pi \times \text{radius} \times \text{slant height}\)
The slant height given is 20 inches, which is also equal to the slant height of the cone. To find the radius of the cone, we need to divide the diameter by 2:
\(\text{radius} = \frac{\text{diameter}}{2}\)
Substituting the values, we get:
\(\text{radius} = \frac{14}{2} = 7\)
Now, we can calculate the curved surface area:
\(\text{Curved Surface Area} = \pi \times 7 \times 20\)
To the nearest hundredth, the curved surface area is approximately \(439.82\) square inches (using \(\pi \approx 3.14\)).
Next, we need to calculate the base area, which is the area of the circular base of the cone. The formula for the area of a circle is:
\(\text{Base Area} = \pi \times \text{radius}^2\)
Substituting the values, we get:
\(\text{Base Area} = \pi \times 7^2\)
To the nearest hundredth, the base area is approximately \(153.94\) square inches (using \(\pi \approx 3.14\)).
To find the total surface area, we add the curved surface area and the base area:
\(\text{Total Surface Area} = \text{Curved Surface Area} + \text{Base Area}\)
\(\text{Total Surface Area} = 439.82 + 153.94\)
To the nearest hundredth, the total surface area of the cone is approximately \(593.76\) square inches.
Therefore, the surface area of the cone is \(593.76\) square inches (rounded to the nearest hundredth).