Question

A sector of a circle with a radius of 15 cm has a central angle of 45°. Another sector of the same circle has a central angle of ∏/4 radians. What is the ratio of the area of the first sector to the area of the second sector?

• A. 1 : 2
• B. 2 : 3
• C. 1 : 1
• D. 3 : 4

Answer 1

Answer:

C. 1 : 1

Area of a sector is proportional to its central angle (when radius is the same):

$\text{Area} = \frac{\theta}{360^\circ}\pi r^2 \quad \text{or} \quad \frac{\theta}{2\pi}\pi r^2$

Since both sectors are from the same circle ((r = 15) cm), we only compare angles.

---

Step 1: Convert angles to same unit

• First sector: (45^\circ)

• Second sector: (\frac{\pi}{4}) radians

Convert second to degrees:

$\frac{\pi}{4} \times \frac{180^\circ}{\pi} = 45^\circ$

---

Step 2: Compare areas

Both sectors have the same central angle (45°) and same radius.

So their areas are equal.

---

Final Answer:

$\boxed{1:1}$