Question : The perimeter of a sector of a circle of radius 7.4 cm is 20.6 cm. The area of this sector is:
Option 1: 42.92 cm2
Option 2: 5.8 cm2
Option 3: 10.73 cm2
Option 4: 21.46 cm2
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Correct Answer: 21.46 cm2
Solution : The radius of the circle = 7.4 cm Let the length of the arc be $l$ cm. The perimeter of the sector = Radius + Length of the arc + Radius $⇒20.6 = 7.4 + l + 7.4$ $⇒l = 20.6 -14.8 = 5.8$ cm Area = $\frac{1}{2} ×\text{ length of arc × radius}$ $=\frac{1}{2}\times 5.8\times 7.4=21.46$ cm$^2$ Hence, the correct answer is 21.46 cm2.
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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 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
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 : The perimeter of a parallelogram is 48 cm. If the height of the parallelogram is 6 cm and the length of the adjacent side is 8 cm. Find its area.
Option 1: 90 cm2
Option 2: 80 cm2
Option 3: 84 cm2
Option 4: 96 cm2
Question : Find the surface area of a sphere whose radius is 3.5 cm. Use $(\left.\pi=\frac{22}{7}\right)$.
Option 1: 154 cm2
Option 2: 152 cm2
Option 3: 146 cm2
Option 4: 160 cm2
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