Chapter 11.3, Problem 25PPS

a.

To determine

To calculate: The area of each sector of silver disk.

Answer to Problem 25PPS

The area of the each sector of ${50}^{\circ }$ angle is 1.74 cm²and the area of the sector of ${260}^{\circ }$ angle is 9.07 cm².

Explanation of Solution

Given information: Radius of the circle is 2 cm. and the angles of sectors are ${50}^{\circ },{50}^{\circ }$ and ${260}^{\circ }$ .

Formula used: Area of sector $=\frac{\mathrm{\theta }}{360}\times \mathrm{\pi }{\mathrm{r}}^2$

  $\mathrm{\theta }=$ Angle of the shaded sector,

  $\mathrm{r}=$ Radius of the circle.

Calculation:

Here, $\mathrm{r}=15$ , ${\mathrm{\theta }}_1={50}^{\circ },{\mathrm{\theta }}_2={50}^{\circ },{\mathrm{\theta }}_3={260}^{\circ }$ and $\mathrm{\pi }=\frac{22}{7}$

Area of sectors,

A₁$=\frac{50}{360}\times \frac{22}{7}\times {\left(2\right)}^2=1.74$

A₂$=\frac{50}{360}\times \frac{22}{7}\times {\left(2\right)}^2=1.74$

A₃$=\frac{260}{360}\times \frac{22}{7}\times {\left(2\right)}^2=9.07$

Hence, the area of the each sector of ${50}^{\circ }$ angle is 1.74 cm²and the area of the sector of ${260}^{\circ }$ angle is 9.07 cm².

b.

To determine

To calculate: Weight of the silver wedge for each earring.

Answer to Problem 25PPS

The weight of the silver wedge for each earring is 319.44 mg.

Explanation of Solution

Given information: Radius of the circle is 2 cm. and the angle of the sector of silver wedge for each earring is ${50}^{\circ }$ .

Calculation: Weight of silver wedge for each earring $=\frac{\mathrm{\theta }}{360}\times$ total weight of silver disk

So, weight of silver wedge for each earring $=\frac{50}{360}\times 2.3=0.31944$ gm $=319.44$ mg.

Hence, weight of the silver wedge for each earring is 319.44 mg.