Chapter 11.3, Problem 7CYU

(a)

To determine

To calculate: The area of the slice (sector geometry) (made by cutting pie into 6 equal spices) of the given circle with diameter 9 inches.

Answer to Problem 7CYU

The area of the each slice of pie is = 10.6 sq inches (nearest to tenth).

Explanation of Solution

Given information:

A pie (circle) with diameter 9 inches and cut the pie in 6 equal slices.

Calculation:

To calculate the required area, use the result

1. Area of the sector with radius r and angle θ is given by

  $\frac{\theta }{360}\times \pi r^2$

Now area of the sector

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

As radius of the circle = half of the diameter.

= $\frac{9}{2}inches$

And to find the value of θ

= $\frac{360}{6}=60$

{Since pie is cut into 6 equal parts, so divide the angle 360 by 6}

Hence by using all these values, we get

= $\frac{60}{360}\times \frac{22}{7}\times \frac{9}{2}\times \frac{9}{2}$

= $\frac{1782}{168}=10.60=10.6$ sq inches (nearest to tenth)

(b)

To determine

To calculate: The money that she will raise after selling 8 slices.

Answer to Problem 7CYU

The money that will raise after selling=$8

Explanation of Solution

Given information:

A pie (circle) that is cut into 6 equal slices.

And the cost of making one slice each=$0.25

Selling price of one slice each=$1.25

And she sells total 8 slices.

Calculation:

To calculate the money that raise after selling

=selling price of 8 slices −cost price of 8 slices

Cost price of each slice=$0.25

Then cost price of 8 slices

=8×$0.25=$2

Selling price of each slice=$1.25

Then selling price of 8 slices=8×$1.25=$10

Hence the money that will raise=$10-$2=$8