Chapter 11.6, Problem 7CE

(a)

To determine

To Compare: The area of two sectors.

Answer to Problem 7CE

Area of sector of bigger circle is four times as much as the smaller circle.

Explanation of Solution

Given: If they have same central angle but radius of one is twice as long as radius of other.

Let the radius of smaller be $y$

Then

Radius of bigger circle be $2y$

Thus

Using area of sector formula.

  $\begin{array}{l}{A}_s=\frac{x}{360}\pi y^2\mathrm{..}(i)\\ $ A_b=\frac{x}{360}\pi {(2y)}^2$A_b=4\cdot \frac{x}{360}\pi y^2\mathrm{...}(ii)\end{array}$

On comparing $(i)and(ii)$

We get to know that

Area of sector of bigger circle is four times as much as the smaller circle.

(b)

To determine

To Compare: The area of two sectors.

Answer to Problem 7CE

Area of sector of bigger central angle is twice the area of sector of smaller sector.

Explanation of Solution

Given: If they have same radius but central angle of one is twice as long as central angle of other.

Let the angle of smaller be $x$

Then

Central angle of bigger circle be $2x$

Thus

Using area of sector formula.

  $\begin{array}{l}{A}_s=\frac{x}{360}\pi r^2\mathrm{..}(i)\\ $ A_b=\frac{2x}{360}\pi {(r)}^2$$ A_b=2\cdot \frac{x}{360}\pi {(r)}^2\mathrm{....}(ii)$\end{array}$

On comparing $(i)and(ii)$

We get to know that

Area of sector of bigger central angle is twice the area of sector of smaller sector.