Question

A pizza parlor cuts its 14-inch (diameter) pizzas into 8 equal slices. What is the size (in square inches) of each slice?
a) 5.5
b) 19.2
c) 44.1
d) 60.4
e) 77.0

Answer 1

Hint: We start solving the problem by drawing the circle to represent the pizza. We then find the area of the whole pizza by using the formula for the area of a circle that is $\pi {{r}^{2}}$ where r is the radius of the circle, which is equal to the half of the diameter. Since the pizza is being divided into 8 equal slices, we have to divide the obtained area by 8 to get the area of each slice as our answer.

Complete step-by-step answer:
In this given question, we are given that a pizza parlor cuts its 14-inch (diameter) pizzas into 8 equal slices. We are asked to find the area of each slice. Let us represent the diameter of the circle as ‘d’.
So, we have $d=14inches$.
Let us draw the circle with diameter 14 inch to show the pizza and its pieces which were cut.

Let us now find the radius (r) of the circle. We know that the radius of the circle is half times the diameter of the circle. According to the problem, we have diameter of the circle as 14 inches.
So, we get \[r=\dfrac{d}{2}\].
$\Rightarrow r=\dfrac{14}{2}$.
$\Rightarrow r=7inches$.
So, we have found the radius of the circle as 7 inches.
Let us find the area of the circle (pizza). We know that the area of the circle is equal to$\pi {{r}^{2}}$. We use $\pi =\dfrac{22}{7}$ in order to solve the problem. Let us assume that the area of the pizza is ‘A’.
Now, we have $A=\pi {{r}^{2}}=\dfrac{22}{7}\times 7\times 7$.
$\Rightarrow A=22\times 7$.
$\Rightarrow A=154inc{{h}^{2}}$.
According to the problem, we need to divide the entire pizza into 8 equal slices. This tells us that the area of the circle is to be divided into 8 equal parts to get 8 slices.
Now, we divide the area A with 8 in order to get the area of each slice. Now, let us assume the area of each slice as ${{A}_{s}}$.
So, we get ${{A}_{s}}=\dfrac{154}{8}$.
$\Rightarrow {{A}_{s}}=19.25inc{{h}^{2}}$.
Let us round off the obtained answer up to 1 decimal place. So, we get the area of each slice as $19.2inc{{h}^{2}}$.
Therefore, we get our correct answer to the question as option (b).

So, the correct answer is “Option b)”.

Note: In this sort of question, we should be careful while rounding off numbers ending with 5. If the previous number of 5 is even, then it won’t be changed but if it is odd then will be increased by 1. We should not always take the value of $\pi $ as $\dfrac{22}{7}$ while solving the problems. We should take the value of $\pi $ as per the requirement of the problem. We should not make calculation mistakes while solving this problem.