Anita needs to construct ten cones for a class project. How many square feet of material will she need? Use 3.14 for π. Enter your answer in the box.
The diameter is 6 and the slant height is 12. What is the surface area?
To find the surface area of a cone, we need to know the radius and slant height. The formula for the surface area of a cone is given by:
Surface Area = πr(r + l)
Given that the diameter is 6, we can find the radius by dividing the diameter by 2:
Radius = 6 / 2 = 3
Now we can calculate the surface area using the formula:
Surface Area = 3.14 * 3(3 + 12)
Surface Area = 3.14 * 3(15)
Surface Area = 3.14 * 45
Surface Area = 141.3
Therefore, Anita will need approximately 141.3 square feet of material to construct ten cones.
To find the surface area of a cone, we need to calculate the lateral surface area and the base area separately.
First, let's find the slant height of the cone. The slant height (l) can be found using the Pythagorean theorem, where l = √(r² + h²), r is the radius of the base, and h is the height of the cone.
In this case, we are given the diameter, which is twice the radius. So, the radius (r) can be calculated by dividing the diameter by 2:
r = diameter / 2 = 6 / 2 = 3 units
Next, we can calculate the slant height (l) using the given values:
l = √(r² + h²) = √(3² + 12²) = √(9 + 144) = √153 ≈ 12.37 units
Now that we have the slant height, let's calculate the lateral surface area (LSA) using the formula LSA = π * r * l:
LSA = 3.14 * 3 * 12.37 ≈ 116.03 square units
Finally, to find the total surface area, we need to also consider the base area (BA) of the cone. The base area can be calculated using the formula BA = π * r²:
BA = 3.14 * 3² = 3.14 * 9 ≈ 28.26 square units
To get the total surface area (TSA) of the cone, we add the lateral surface area and the base area:
TSA = LSA + BA ≈ 116.03 + 28.26 = 144.29 square units
So, Anita will need approximately 144.29 square feet of material to construct ten cones.
Solving for the lateral surface area of one cone:
LSA = (3.14) (3) [√(12²+3²)] = 116.52 sq ft.
Since she needs 10 cones:
10 * 116.52 sq. ft = 1,165.2 sq ft.
She will need 1,165.2 sq ft of m
the area of each cone will be a = πrs
where r is the radius of the base.