John bought a conical hat on a recent trip to central Vietnam. The basic frame of the hat is 16 hoops of bamboo that gradually diminish in size. The hat is covered in palm leaves. If the hat has a diameter of 50 centimeters and a slant height of 32 centimeters, what is the lateral area of the conical hat?
You want the lateral surface area of a cone
= π r s, where r is the radius, and s is the "slant" height
= π(25)(32)
= cm^2
2513.27 cm^2
To find the lateral area of the conical hat, we need to calculate the curved surface area of the conical part.
The curved surface area of a cone can be calculated using the formula:
Lateral Area = π × r × l
Here, r is the radius of the hat's base, and l is the slant height.
First, we need to calculate the radius. The diameter is given as 50 centimeters, so the radius is half of that:
Radius (r) = Diameter / 2 = 50 cm / 2 = 25 cm
Now, we can use the values of the radius (r) and the slant height (l) in the formula to get the lateral area:
Lateral Area = π × r × l
Lateral Area = π × 25 cm × 32 cm
To get the final answer, we can use the value of π (pi), which is approximately 3.14, and perform the calculation:
Lateral Area = 3.14 × 25 cm × 32 cm
After performing the multiplication, we have:
Lateral Area = 3.14 × 800 cm^2
So, the lateral area of the conical hat is approximately 2512 cm^2.