Question : The area of a sector of a circle is 616 cm2 with a central angle of 10°. The radius of the circle is_____. (use $\pi=\frac{22}{7}$)
Option 1: 84 cm
Option 2: 21 cm
Option 3: 48 cm
Option 4: 28 cm
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Correct Answer: 84 cm
Solution : The area of a sector of a circle is 616 cm2 with a central angle of 10°. Let the radius of the circle = $r$ cm We know, The area of a sector of a circle with a central angle of $\theta=(\pi r^2×\frac{\theta}{360^\circ})$ According to the question, $(\pi r^2×\frac{10^\circ}{360^\circ})=616$ $⇒\frac{22}{7}×r^2×\frac{10^\circ}{360^\circ}=616$ $⇒r^2=616×\frac{7}{22}×\frac{360^\circ}{10^\circ}$ $⇒r=\sqrt{7056}$ $\therefore r=84$ cm Hence, the correct answer is 84 cm.
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Question : The perimeter of a minor sector of a circle of radius 5 cm is 15.5 cm. Find the area of the minor sector (use $\pi=\frac{22}{7}$ ).
Option 1: 17.53 cm2
Option 2: 13.75 cm2
Option 3: 13.57 cm2
Option 4: 17.35 cm2
Question : The area of a sector of a circle that subtends a 22.5° angle at the centre is given as 346.5 cm². What will be the radius (in cm) of the circle? [Use $\pi=\frac{22}{7}$]
Option 1: 35
Option 2: 45
Option 3: 42
Option 4: 48
Question : What will be the perimeter (in cm) of the sector of a circle of radius 4.9 cm having a central angle 144° (use $\pi=\frac{22}{7})?$
Option 1: 21.12
Option 2: 23.32
Option 3: 23.23
Option 4: 22.12
Question : The circumference of a circle is 132 cm. The area of the circle is: (Take $\pi=\frac{22}{7}$)
Option 1: 1380 cm2
Option 2: 1322 cm2
Option 3: 1086 cm2
Option 4: 1386 cm2
Question : A copper wire is bent in the form of a square and it encloses an area of 30.25 cm2. If the same wire is bent to form a circle, then find the area of the circle. [Use $\pi=\frac{22}{7}$]
Option 1: 38.50 cm2
Option 2: 42.25 cm2
Option 3: 35 cm2
Option 4: 30.25 cm2
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