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 : 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 : If two concentric circles have radii of 5 cm and 3 cm, then the length of the chord of the larger circle that touches the smaller circle is:
Option 1: 6 cm
Option 2: 7 cm
Option 3: 10 cm
Option 4: 8 cm
Question : A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. The area of the circle is: (take $\pi=\frac{22}{7}$)
Option 1: 125 cm2
Option 2: 230 cm2
Option 3: 550 cm2
Option 4: 616 cm2
Question : P and Q are centre of two circles with radii 9 cm and 2 cm respectively, where PQ = 17 cm. R is the centre of another circle of radius $x$ cm, which touches each of the above two circles externally. If $\angle PRQ=90^{\circ}$, then the value of $x$ is:
Option 1: 4 cm
Option 2: 6 cm
Option 3: 7 cm
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
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