Question : The ratio of the areas of two squares one having double its diagonal than the other is:
Option 1: 3 : 2
Option 2: 2 : 1
Option 3: 4 : 1
Option 4: 3 : 1
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Correct Answer: 4 : 1
Solution : Let the diagonal of the 1st square be $2x$. Area of 1st square = $\frac{1}{2}$ × (product of diagonals) = $\frac{1}{2}×(2x)^2$ Since the diagonal of the 2nd square is half of the diagonal of the 1st square i.e. $x$. So, the area of 2nd square = $\frac{1}{2}$ × (product of diagonals) = $\frac{1}{2}×x^2$ So, Area of 1st square : Area of 2nd square = $\frac{1}{2}×4x^2$ : $\frac{1}{2}×x^2$ = 4 : 1 Hence, the correct answer is 4 : 1.
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Question : If the ratio of areas of two circles is 4 : 9, then the ratio of their circumferences will be:
Option 2: 9 : 4
Option 3: 2 : 3
Option 4: 4 : 9
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?
Option 1: 5 : 17
Option 2: 7 : 20
Option 3: 6 : 19
Option 4: 20 : 7
Question : Two cylinders have their heights in the ratio 1 : 2 and their radii in the ratio 2 : 1. What is the ratio of their volumes?
Option 1: 3 : 1
Option 2: 1 : 3
Option 3: 2 : 1
Option 4: 1 : 2
Question : The ratio of the total surface areas of the two cubes is 49 : 81. What is the ratio of their volumes?
Option 1: 343 : 729
Option 2: 294 : 486
Option 3: 7 : 9
Option 4: 49 : 121
Question : The surface areas of the two spheres are in the ratio of 64 : 81. Find the ratio of their volumes, in the order given.
Option 1: 512 : 729
Option 2: 64 : 729
Option 3: 8 : 81
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