Chapter 11, Problem 14STP

a.

To determine

To calculate the square inches of dough to make a large pizza.

Answer to Problem 14STP

Square inches of dough required or the area of the large pizza is $154$ square inches.

Explanation of Solution

Given information:

Given figure is a circle with diameter $d=14$ inches. Hence radius $r=\frac{d}{2}$

  $=\frac{14}{2}$

  $=7$ inches.

Formula used:

Area of a circle $a=\pi \times r^2$

Here ‘r’ is the radius of the circle.

For calculation, take the value of $\pi =\frac{22}{7}$ .

Calculation:

Area of a circle

  $a=\pi \times r^2$

Formula for the area of a circle.

  $=\frac{22}{7}\times 7^2$

Putting the values in the formula.

  $=\frac{22}{7}\times \text{49}$

Simplifying the same.

  $=22\times 7$

On solving the expression.

  $a=154$ square inches.

b.

To determine

To calculate the circumference of the circular large pizza.

Answer to Problem 14STP

Circumference of the large circular pizza is $\text{44}$ inches.

Explanation of Solution

Given information:

Given figure is a circle with diameter $d=14$ inches. Hence radius $r=\frac{d}{2}$

  $=\frac{14}{2}$

  $=7$ inches.

Formula used:

Circumference of a circle $c=2\times \pi \times r$

Here ‘r’ is the radius of the circle.

For calculation, take the value of $\pi =\frac{22}{7}$ .

Calculation:

Circumference of a circle.

  $c=2\times \pi \times r$

Formula to compute the circumference of a circle.

  $=2\times \frac{22}{7}\times 7$

Putting the values in the formula.

  $=2\times 22$

Multiplying the expression.

  $c=\text{44}$ inches.

c.

To determine

To calculate the central angle of each pizza slice.

Answer to Problem 14STP

Central angle of each pizza slice is $45°$ .

Explanation of Solution

Given information:

The large is a circle in shape, and is cut into 8 equal slices.

A circle, when cut into smaller sectors have central angles. These central angles when added back, produce a measure of $360°$ . Consider this, if all the slices are rearranged back, they would form a circle resembling the original large pizza.

In this case, all the slices are equal and there are 8 such equal slices. Hence, divide $360°$ by the number of slices to obtain the central angle of each slice.

Consider the central angle of each slice to be ‘g’.

So, $g=\frac{360°}{8}$

  $=45°$

This is the central of each pizza slice.