Answer:
A = 326,73 cm²
Explanation:
The area of a circular cone is area of the base (A₁ ) plus area lateral ( area of a circular sector of radius the slant height )
Then we proceed to calculate the area of the base A₁
diameter of circular base is 8 cm then the radius is 4 cm and the area is:
A₁ = π*r² = 3,14* (4)²
A₁ = 3,1416*16 = 50,2656 cm²
Now Lateral area of the cone (A₂) is equal to the area of a circular sector with radius the slant height. We will calculate it, taken into account that this circular sector is part of a circle of radius the slant height.
Between the area of circular sector with radius the slant height and the area of the circle with the same radius there is a linear relation. That is we can calculate area of a circular sector by rule of three as follows:
The length of the circular sector is the length of the circle of the base of the cone, that is:
L = 2*π*(4)
L = 2*3,1416*4
L = 25,1328 cm
Then we have a circular sector of length 25,1328 cm
The area of the circle of radius 22 cm is:
A(c) = π*(22)² ⇒ A(c) = 1520,5344 cm²
And the length of this circle is:
L(c) = 2*π*(22) ⇒ 138,2304 cm
Then we apply a rule of three
For a length of 138,2304 cm ⇒⇒⇒ (area) 1520,5344 cm²
Then for a length of 25,1328 cm ⇒⇒⇒(area) A₂ (??)
Therefore:
A₂ = (25,1328)*1520,5344)/ 138,2304
A₂ = 276,4608 cm²
Then total area of the cone is:
A = A₁ + A₂
A = 50,2656 +276,4608
A = 326,7264 cm²
Round answer A = 326,73 cm²