Question : Nine times the area of a circle is the same as the three times the area of a square. What is the ratio of the diameter of the circle and the diagonal of the square?
Option 1: $\sqrt{2}: \sqrt{3 \pi}$
Option 2: $2: \sqrt{3 \pi}$
Option 3: $2: 3 \pi$
Option 4: $\sqrt{5}: \sqrt{7 \pi}$
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Correct Answer: $\sqrt{2}: \sqrt{3 \pi}$
Solution : Let the radius of the circle be $r$ and the side of the square be $a$. According to the question, ⇒ $9 \times \pi r^2 = 3 \times a^2$ ⇒ $a = r \sqrt{3\pi}$ The diameter, $d$ of the circle = $2r$ The diagonal, $D$ of the square = $a\sqrt{2}$ Putting the value of $a$, we get: $D = a\sqrt{2} = r\sqrt{6\pi}$ Therefore, the ratio of the diameter of the circle to the diagonal of the square is: $\frac{d}{D} = \frac{2r}{r\sqrt{6\pi}} = \frac{\sqrt2}{\sqrt{3\pi}}$ Hence, the correct answer is $\sqrt{2}: \sqrt{3 \pi}$.
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Question : The area of a square is 1296 cm2 and the radius of a circle is $\frac{7}{6}$ of the length of a side of the square. What is the ratio of the perimeter of the square and the circumference of the circle? [Use $\pi=\frac{22}{7}$ ]
Question : If the circumference of a circle is equal to the perimeter of a square, and the radius of the given circle is positive, then which of the following options is correct?
Question : One of the diagonals of a rhombus is 70 percent of the other diagonal. What is the ratio of the area of the rhombus to the square of the length of the larger diagonal?
Question : The curved surface area is thrice as big as the base area of a cone. If the diameter of the cone is 1 cm. Then what is the total surface area (in cm2) of the cone?
Question : What is the area of a circle with a diameter of $12~\text{mm}$?
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