Question

Σ
Q31. Observe the pie chart given
below and answer the following
questions: (i) The central angle for
sector A is (ii) What is the difference
between the central angles for sector
B and sector C ?

Answer 1

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Answer 2

Given:

A circle with sectors A, B, and C

Percentage of sector A = 30%

Percentage of sector B = 40%

Percentage of sector C = 30%

To Find:

(i) The central angle for sector A

(ii)The difference between the central angles for sector B and sector C

Solution

• For finding the central angle for each sector, we will use the following property of a circle:

                     "Total central angle of a circle is 360°".

What is a sector of a circle?

• A sector is the portion of a circle enclosed by two radii and an arc.

Now, we will find the answer to each question by the following steps:

Step 1: Finding the central angle of sector A.

• It is given that sector A occupies 30% of the circle.

      So, the central angle of A = $\frac{30}{100}$ × 360

                                 ∠A = 108°

Hence, the central angle for sector A is 108°.

Step 2: Finding the central angle of sector B.

• It is given that sector B occupies 40% of the circle,

     So, the central angle of sector B = $\frac{40}{100}$ × 360°

                                                            = 144°

Hence, the central angle for sector B is 144°.

Step 3: Find the central angle of sector C.

• It is given that sector C occupies 30% of the circle,

     So, the central angle of sector B = $\frac{30}{100}$ × 360°

                                                            = 108°

Hence, the central angle for sector C is 108°.

Step 4: Calculate the difference between the angles of sectors B and C.

• We know from Step 2 and Step 3 that

       The central angle of sector B = 144°

      and Central angle of sector C = 108°

          ∴ Difference = 144° - 108°

                                = 36°

Hence, the difference between the central angles of sectors B and C is 36°.

Hence,

(i) The central angle for sector A is 108°

(ii) The difference between the central angles of Sector B and C is 36°.