Area of a sector and segment of a circle MCQs

Q1. Find the area of the sector: radius 7 cm, angle 60 degrees (pi = 22/7):

• A.7.33
• B.154
• C.3.67
• D.25.67

Answer: D. 25.67

Q2. Find the area of the sector: radius 7 cm, angle 135 degrees (pi = 22/7):

• A.8.25
• B.16.5
• C.57.75
• D.154

Answer: C. 57.75

Start by listing the data - 7 cm (math, chapter 'Areas Related to Circles'). The unknown we need is Find the area of the sector: radius 7 cm, angle 135 degrees (pi = 22/7). From the chapter we use the relation: recall that in a right triangle with legs p, b and hypotenuse h: sin = p/h, cos = b/h, tan = p/b. Putting the numbers in: so the answer = 57.75. Identify the side-pair demanded and read off the ratio. So the correct choice is C) 57.75. As for the others, option A) '8.25' misses the point - Wrong: a common multi-step slip gives this; option B) '16.5' is incorrect: Wrong: a step was skipped or HCF/LCM swapped.

Q3. Find the area of the sector: radius 7 cm, angle 210 degrees (pi = 22/7):

• A.25.67
• B.12.83
• C.89.83
• D.154

Answer: C. 89.83

Given 7 cm, asked for Find the area of the sector: radius 7 cm, angle 210 degrees (pi = 22/7). By substitute the standard values sin 30 = 1/2, sin 45 = 1/sqrt 2, sin 60 = sqrt 3/2, cos 30 = sqrt 3/2, cos 60 = 1/2, tan 45 = 1. substitute the standard values sin 30 = 1/2, sin 45 = 1/sqrt 2, sin 60 = sqrt 3/2, cos 30 = sqrt 3/2, cos 60 = 1/2, tan 45 = 1 → hence the value = 89.83. perform the arithmetic in the given expression. Hence option C) 89.83. Others fail: option A) '25.67' is incorrect: Wrong: a step was skipped or HCF/LCM swapped; option B) '12.83' is incorrect: Wrong: a common multi-step slip gives this.