Chapter SH, Problem 7.8.2EP

(a)

To determine

To calculate: To find how many degrees would Miguel need to use for the central angle on his circle graph for the Study sector

Answer to Problem 7.8.2EP

Central angle for Study sector is ${36}^{\circ }$

Explanation of Solution

Given information: Given that Miguel studied for $16.8$ hours in a week

Formula Used:

Portion is circle graph is calculated

  $TypeA=\frac{Portion}{Total}\times 100$

Calculation:

Given that Miguel studied for $16.8$ hours in a week

Total hours in week $=7\times 24=168$

Central angle on circle graph for Study sector is calculated as

  $\begin{array}{l}Angle=\frac{16.8}{168}\times {360}^{\circ }\\ Angle=\frac{1}{10}\times {360}^{\circ }\\ Angle={36}^{\circ }\end{array}$

Conclusion:

Hence, central angle is ${36}^{\circ }$

(b)

To determine

To calculate: To find how many hours did Gabriel spend practicing the piano during the week and round to the nearest hundredth

Answer to Problem 7.8.2EP

Hours spent byGabriel in practicing the piano is $11.67$ hours

Explanation of Solution

Given information: Gabriel used ${25}^{\circ }$ for the central angle for the sector labelled Piano

Formula Used:

Portion is circle graph is calculated

  $TypeA=\frac{Portion}{Total}\times 100$

Calculation:

Given that Gabriel used ${25}^{\circ }$ for the central angle for the sector labelled Pianoin a week

Total central angle $={360}^{\circ }$

Central angle on circle graph for Study sector is calculated as

  $Angle=\frac{x}{168}\times {360}^{\circ }$

Here $Angle={25}^{\circ }$

Substituting the values,

  $\begin{array}{l}{25}^{\circ }=\frac{x}{168}\times {360}^{\circ }\\ x=\frac{{25}^{\circ }\times 168}{{360}^{\circ }}\\ x=\frac{4200}{360}\\ x=11.666\\ x=11.67\end{array}$

Conclusion:

Hence, hours spend in practicing piano is $11.67$ hours