Question

The cone has a base diameter of 20cm and a slant height of 25 cm.

Answer 1

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