Question

The area of a minor sector of a circle is 3.85 cm². The measure of its central angle is 36°. Find the radius of circle.

Area of minor sector = 3.85 cm²

Measure of its central angle (θ) = 150°

Let, its radius be r

Area of minor sector = `θ/(150^circ) xx square`

`3.85 = (36^circ)/(360^circ) xx 22/7 xx r^2`

`r^2 = (square xx square xx square)/square`

r² = 12.25

r = `square`

Answer 1

Given: Area of minor sector A = 3.85 cm², central angle θ = 36°, radius = r.

Step-wise calculation:

1. Use area formula:

\[A = \frac{θ}{360°} \times \boxed{πr^2}\]

2. Substitute values:

`3.85 = 36/360^circ × 22/7 × r^2`

3. Simplify factor:

`36/360 = 1/10`

So, `3.85 = 1/10 xx 22/7 × r^2`

4. Solve for r²:

\[r^2 = \frac{\boxed{3.85} \times \boxed{10} \times \boxed{7}}{\boxed{22}}\]

= `(38.5 xx 7)/22`

5. Compute:

`38.5/22 = 1.75`

So, r² = 1.75 × 7

= 12.25

6. Take square root:

`r = sqrt(12.25)` 

= \[\boxed{3.5}\]

The radius of the circle is 3.5 cm.