Question

Question 31 (5 points) Find the area of the shaded portion if we know the outer circle has a diameter of 4 m and the inner circle has a diameter of 1.5 m. O O 10.8 m2 O 12.6 m2 O 43.2 m2 O 1.8 m2

Answer 1

The shaded portion area A corresponds to the area Ao of the outer circle minus the area Ai of the inner circle:

A = Ao - Ai

Also, the area of each circle of radius r is given by:

π r²

where the radius r is half the diameter d.

So, using r = d/2 in the above formula, we obtain:

π r² = π (d/2)² = (π/4) d²

Now, replacing each area with the corresponding diameter, we find:

A = Ao - Ai

= (π/4) 4² - (π/4) 1.5²

= (π/4) (4² - 1.5²)

= (π/4) (16 - 2.25)

= (π/4) (13.75)

≅ 10.799

Rounding the result to one decimal place, we find the answer:

10.8 m²