Answer:
Explanation:
Find the slant height (l) of the cone:
The slant height is the distance from the tip of the cone to the base edge along the curved surface. You can use the Pythagorean theorem to find it if you have the radius (r) and the height (h) of the cone. The formula is:
l = √(r^2 + h^2)
Calculate the circumference (C) of the base of the cone:
The circumference of the base is given by:
C = 2πr
Find the central angle (θ) of the sector:
The central angle θ can be calculated using trigonometry:
θ = 2 * atan(r / h)
Calculate the curved surface area (A_c) of the sector:
The curved surface area of a sector is given by the formula:
A_c = (θ/360) * π * r^2
Finally, calculate the surface area of half the cone by adding the curved surface area to the area of the circular base (half of the base area):
Surface Area = A_c + (1/2) * C * l
Now, you can plug in the values for r and h, and follow these steps to calculate the surface area of half a cone. Remember to use consistent units for your measurements.
Here's a summary of the formulas for reference:
Slant height (l): l = √(r^2 + h^2)
Circumference of the base (C): C = 2πr
Central angle (θ): θ = 2 * atan(r / h)
Curved surface area of the sector (A_c): A_c = (θ/360) * π * r^2
Surface area of half the cone: Surface Area = A_c + (1/2) * C * l