Respuesta :
Answer:
The area of the cone not painted is approximately 196.35 cm²
Step-by-step explanation:
The question relates to similar shapes;
We have;
The base diameter of the cone, D₁ = 20 cm
The slant height of the cone, l₁ = 25 cm
The height at which the circle is drawn, 10 cm above the base, we have; l₂ = 25 cm - 10 cm = 15 cm
Let 'x' represent the diameter of the circle formed by the drawn circle, we have;
By similar triangles, we get;
D₁/l₁ = x/l₂
x = l₂ × D₁/l₁
20/25 = x/15
x = (20/25) × 15 = 12
The curved surface area of the cone, A = π·r·l
The area of the curved surface of the entire cone, A₁ = π·r₁·l₁
r₁ = D₁/2
Therefore, we get, A₁ = π × 20/2 × 25 = 250·π
A₂ = π × 15/2 × 25 = 187.5·π
The area of the cone not painted, A = A₁ - A₂
∴ A = 250·π - 187.5·π = 62.5·π
The area of the cone not painted, A = 62.5·π ≈ 196.35
The area of the cone not painted ≈ 196.35 cm²
