Question

The surface area of a cone is 1130 ft2. The radius is 10 ft. What is the lateral area of the cone to the nearest whole number? Use 3.14 for π

Answer 1

I hope this helps you

Answer 2

Lateral surface area is about 815.7 ft² .

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

`(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 .