The design for a new cone-shaped closed container is shown below. What is the surface area of this container, in square inches? On a picture of a cone with a slant height of 6 in. and the diameter of 4 in.?
The XYZ Company sells hats and will monogram them if customers choose. The price for each monogram varies depending on how many hats a customer would like to have monogrammed. The monogram prices for several order sizes are shown on a chart from the XYZ Company, which are: 1 hat is $5.00; 2 hats are $4.50; 3 hats are $4.00; 4 hats are $3.50; 5 hats are $3.00, and 6 hats are $2.50. Which of the equations best expresses the relationship of price per monogram (for all nonnegative values of p) to number of hats monogrammed shown in the information? Is it p=$5.00-(n-1)$0.50; p=$5.00-n($0.50); p=(n-1)$5.00; p=$0.50(10n); or p=$5.00(10n)?
To find the surface area of a cone, we need to determine the area of the circular base and the lateral surface area.
First, let's calculate the area of the circular base. The base of the cone is a circle, and its area can be found using the formula:
Area of a circle = π * radius^2
The diameter of the cone is given as 4 inches, so the radius is half of that, which is 2 inches.
Area of the circular base = π * (2 in)^2 = π * 4 in^2
Next, let's calculate the lateral surface area. The lateral surface of a cone is a curved surface that forms the sides of the cone. The formula to calculate the lateral surface area is:
Lateral surface area of a cone = π * radius * slant height
The radius is 2 inches (as calculated earlier), and the slant height is given as 6 inches.
Lateral surface area of the cone = π * 2 in * 6 in = 12π in^2
Now that we have the area of the circular base and the lateral surface area, we can find the total surface area of the cone by summing these two areas:
Total surface area = Area of the circular base + Lateral surface area
Total surface area = π * 4 in^2 + 12π in^2
Total surface area = 16π in^2
So, the surface area of the cone-shaped closed container is 16π square inches.
To find the surface area of a cone, you need to consider two parts: the area of the curved surface (lateral area) and the area of the base.
1. Curved Surface Area (Lateral Area):
The formula to calculate the lateral area of a cone is A = π * radius * slant height.
In this case, the diameter is given as 4 inches, so the radius can be calculated as half of the diameter:
Radius = Diameter / 2 = 4 in / 2 = 2 in.
The slant height is provided as 6 inches.
Now, plug the values into the formula:
Lateral Area = π * 2 in * 6 in = 12π in^2.
2. Base Area:
The base of the cone is a circle, and the formula for the area of a circle is A = π * radius^2.
Using the radius we calculated earlier, the base area can be found:
Base Area = π * (2 in)^2 = 4π in^2.
3. Total Surface Area:
The total surface area of the cone is the sum of the lateral area and the base area:
Total Surface Area = Lateral Area + Base Area
= 12π in^2 + 4π in^2
= 16π in^2.
So, the surface area of the given cone-shaped container is 16π square inches.