Question : Four circles of equal radii are described around the four corners of a square so that each touches two of the other circles. If each side of the squares is 140 cm, then the area of the space enclosed between the circumference of the circle is: (Take $\pi=\frac{22}{7}$)
Option 1: 4200 cm2
Option 2: 2100 cm2
Option 3: 7000 cm2
Option 4: 2800 cm2
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Correct Answer: 4200 cm2
Solution : Given: Four circles of equal radii are described around the four corners of a square so that each touches two of the other circles. Each side of the squares is 140 cm. Each side of the square ($a$) = 140 cm The radius of the circles ($r$) = 70 cm The area of the enclosed space = (Area of the square) – (Area of 4 quadrants i.e. the area of a circle) So, the area of the enclosed space = $a^2 - \pi r^2$ = $140^2-(\frac{22}{7}×70×70)$ = $19600 – 15400$ = 4200 cm2 Hence, the correct answer is 4200 cm2.
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Question : The base of a right prism is a square having a side of 15 cm. If its height is 8 cm, then find the total surface area.
Option 1: 940 cm2
Option 2: 920 cm2
Option 3: 900 cm2
Option 4: 930 cm2
Question : The centroid of a $\triangle ABC$ is G. The area of $\triangle ABC$ is 60 cm2. The area of $\triangle GBC$ is:
Option 1: 10 cm2
Option 2: 30 cm2
Option 3: 40 cm2
Option 4: 20 cm2
Question : Two concentric circles are of radii 10 cm and 6 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Option 1: 8 cm
Option 2: 16 cm
Option 3: 12 cm
Option 4: 9 cm
Question : The circumference of the two circles is 110 cm and 330 cm respectively. What is the difference between their radii?
Option 1: 70 cm
Option 2: 15 cm
Option 3: 46 cm
Option 4: 35 cm
Question : The circumference of the two circles is 264 cm and 396 cm respectively. What is the difference between their radii?
Option 1: 25 cm
Option 2: 32 cm
Option 3: 16 cm
Option 4: 21 cm
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