LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

PIE CHART - PROBLEM & SOLUTION

__PIE CHART - PROBLEM & SOLUTION -__

**Example.1) Observe the following pie chart that represents the money spent by Ana
at the funfair. The indicated color
shows the amount spent on each category. The total value of the data
is 20 and the amount spent on
each category is interpreted as follows:**

**· Ice Cream - 4**

**· Toffees - 4**

**· Popcorn - 2**

**· Rides - 10**

**Ans.) To convert
this into pie chart percentage, we apply the formula:-**

** (Frequency ÷ Total Frequency) × 100**

**Let us convert the above data into a percentage.**

**Amount spent on rides: (10/20) × 100 = 50%**

**Amount spent on toffees: (4/20) × 100 = 20%**

**Amount spent on popcorn: (2/20) × 100 = 10%**

**Amount spent on ice-cream: (4/20) × 100 =
20% (Ans.)**

**Example.2) Observe
the following pie chart that recommends
a low-carb diet on
a day.**

**Ans.) We
measure the angles of each slice. We get that Protein measures 180°, Carb measures 108°, and Fats
measures 72°.**

**To find the percentage, we divide each angle by 360 and
multiply it by 100.**

** Protein = (180/360) × 100 = 50%**

**Carb = (108/360)
× 100 = 30%**

**Fats = (72/360) × 100 = 20%**

__Example.3)__ The pie chart shown below shows the percentages of types of
transportation used by 500 students
to come to school. With this given information, answer the following questions:

**a) How many students
come to school by bicycle?**

**b) How many students
do not walk to school?**

**c) How many students come to school by bus and car?**

**Ans.) **

**a) The students
who come by bicycle = 25%; (25/100) × 500 = 25 × 5
= 125.**

**b) The students
who do not walk to school- We need to add the values of all the remaining means,
i.e., bus + car + bicycle
= 26 + 32 + 25 = 83.**

**Hence, (83/100)
× 500 = 83 × 5 = 415 students do not walk to school.**

**c) The students
who come by bus and car [(32 + 26)/100]
× 500 = 58 × 5
= 290.**

**Example.4) The following chart shows the various activities
done by Diana in a week.**

**a) Calculate the
central angle subtended at sleeping. **

**b) Find the portion
of time spent by Diana at
school. **

**c) Find the central
angle subtended in playing.**

**Ans.)**

** a) Time spent in sleeping = 34%; (34/100) × 360 = 122.4°.
Therefore, the central angle subtended
at sleeping = 122.4°.**

**b) Time spent at school = 25%; 25/100 = 1/4. Therefore, she
spends 1/4th of her time in school.**

**c) Time spent on playing = 8%; (8/100) × 360 = 28.8°.
Therefore, the central angle subtended
at playing = 28.8°.**

**Example.5) The pie chart
shows the favorite subjects of students in a class. Using the information given in the pie
chart, find the percentage of students who chose
English.**

**Ans.) Let's
first determine the percentage of students who chose English by looking at the
pie chart.**

**We know that 144° + 36° + 72° + 108°= 360°**

**The percentage of students who chose English:- (72/360) ×
100 = 20 Therefore, the percentage of students who chose English
= 20% (Ans.)**

**Example.6) A pie chart is
divided into 3 parts with the angles measuring as x, 4x, and 5x respectively. Find the value of x in
degrees.**

**Ans.)**

**We know, the
sum of all angles in a pie chart
would give 360º as result.**

**⇒ x + 4x + 5x = 360º**

**⇒ 10 x = 360º**

**⇒ x = 360º/10**

**⇒ x = 36º**

**Therefore, the value of x is
36º.**