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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Correct Answer: 38.50 cm2
Solution : Given, the area of the square formed by copper wire = 30.25 cm2 Area of square = s2 where s is the side of the square. ⇒ 30.25 = s2 ⇒ s = 5.5 cm Now, total length of wire = 4s = 4 × 5.5 = 22 cm Let $r$ be the radius of the circle. Length of copper wire = Perimeter of circle formed ⇒ 4s = 2$\pi r$ ⇒ 22 = $2(\frac{22}{7}) r$ ⇒ $r$ = 3.5 cm Area of required circle = $\pi r^2$ = $\frac{22}{7}\times 3.5\times 3.5$ = 38.50 cm2 Hence, the correct answer is 38.50 cm2.
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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 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 total surface area of a solid hemisphere of diameter 14 cm is (use $\pi=\frac{22}{7}$ ):
Option 1: 522 cm2
Option 2: 462 cm2
Option 3: 428 cm2
Option 4: 584 cm2
Question : The total surface area of a cylinder whose radius is 6 cm and height is 8 cm is: (Use $\pi=\frac{22}{7}$)
Option 1: 528 cm2
Option 2: 575 cm2
Option 3: 658 cm2
Option 4: 625 cm2
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