Question

A circular pizza is divided into 3 equal parts, one piece of pizza is taken out. Estimate the degree measure of the single peice of pizza and convert the measure into radians. What is the radian measure of the angle of the remaining part of the pizza

Answer 1

Given:

A circular pizza is divided into 3 equal parts, one piece of pizza is taken out.

To find:

• Degree measure of the single peice of pizza and convert the measure into radians.

• The radian measure of the angle of the remaining part of the pizza

Diagram:

$\boxed{\setlength{\unitlength}{1cm}\begin{picture}(6,6)\put(3,3){\circle{1.4}}\put(3,3){\line(1,-1){0.5}}\put(3,3){\line(-1,-1){0.5}}\put(2.75,2.5){ \angle\theta }\put(2.5,3.25){ \angle\alpha }\put(2.5,1){Pizza}\end{picture}}$

Calculation:

Angle of the whole pizza = 360° ,

Now, it has been divided into 3 parts and 1 part has been taken out.

So, the angle of the single piece

$\angle \theta = \dfrac{ {360}^{ \circ} }{3} = {120}^{ \circ}$

In order to convert to radians:

$\angle \theta ={120}^{ \circ} \times \bigg( \dfrac{\pi}{ {180}^{ \circ} } \bigg)$

$\boxed{ = > \angle \theta = \dfrac{2\pi}{3} \: rad}$

So, radian measure of the rest of the pizza is:

$\angle \alpha = 2\pi - \dfrac{2\pi}{3}$

$\boxed{ = > \angle \alpha = \dfrac{4\pi}{3} \: rad}$