Question

The area of a sector of a circle with radius 7 cm and central angle 90° is :

• A. 38.5 cm²
• B. 35.2 cm²
• C. 40.5 cm²
• D. 42.62 cm²

Answer 1

Answer:

A. 38.5 cm²

Area of a sector:

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

Given:

• (r=7) cm

• $(\theta=90^\circ)$

$=\frac{90}{360}\times \pi \times 7^2$

$=\frac{1}{4}\times \pi \times 49$

$=\frac{49\pi}{4}$

Using $(\pi=\frac{22}{7}):$

$\frac{49}{4}\times \frac{22}{7}$
$=\frac{154}{4}$
$=38.5$

So, the area of the sector is:

$\boxed{38.5\ \text{cm}^2}$