Question

The diameter of the larger circle is 12.5 cm. The diameter of the smaller circle is 3.5 cm.

What is the best approximation for the area of the shaded region?

Use 3.14 to approximate pi.

(a) 28.26 cm²
(b) 113.04 cm²
(c) 132.27 cm²
(d) 254.34 cm²

also could you explain an alternative to doing this, or an easier way because i don't understand what I am supposed to solve.

Answer 1

If the diameter of the smaller circle is 3.5cm, that means the radius is 1.75cm.

The area of the smaller circle is π × 1.75², which is ≈ 9.62112750162.

The diameter of the larger circle is 12.5 cm, so the radius would be half that, which is 6.25cm. The area of the larger circle would be π × 6.25², which is ≈ 122.718463031.

So now that we know the area of the larger circle and the smaller circle, we can find the area of the shaded region by subtracting the area of the smaller circle from the area of the larger circle, which is basically just 122.718463031 - 9.62112750162, which is = 113.097336. The closest answer here is 113.04, hence the answer is 113.04cm².