Answer:
Lateral surface area is about 815.7 ft² .
Step-by-step explanation:
Given : The surface area of a cone is 1130 ft2. The radius is 10 ft.
To find : What is the lateral area of the cone to the nearest whole number.
Solution : We have given that
surface area of a cone = 1130 ft².
Radius of cone = 10 ft.
Surface area of cone = area of base + lateral surface area +
Surface area of cone = \(\pi (radius)^{2} + \pi * radius * height\).
Plugging the values
1130 = \(3.14 (10)^{2} + 3.14* 10 * height\).
1130 = 314 + 31.4 slant height.
On subtracting 314 from both sides
1130 - 314 = 31.4 slant height.
816 = 31.4 * slant height
On dividing by 31.4 both sides
\(\frac{816}{31.4}\) = slant height
25.98 ft = slant height
Now lateral surface area = \(\pi * radius * slant\ height\).
Plugging the values of radius and slant height
Lateral surface area = \(3.14 * 10 * 25.98\).
Lateral surface area = 815.772 ft²
about 815.7 ft²
Therefore, Lateral surface area is about 815.7 ft² .
