Question : The diagonals of two squares are in the ratio of 3 : 7. What is the ratio of their areas?
Option 1: 3 : 7
Option 2: 9 : 49
Option 3: 4 : 7
Option 4: 7 : 3
Correct Answer: 9 : 49
Solution : The area (A) of a square can be expressed in terms of its diagonal by, $A = \frac{d^2}{2}$ If the diagonals of two squares are in the ratio 3 : 7. The ratio of their areas will be the square of the ratio of their diagonals, $=\left(\frac{3}{7}\right)^2 = \frac{9}{49}$ Hence, the correct answer is 9 : 49.
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Question : The radii of two cylinders are in the ratio of 4 : 5 and their heights are in the ratio of 5 : 2. The ratio of their volume is:
Option 1: 9 : 4
Option 2: 2 : 1
Option 3: 9 : 7
Option 4: 8 : 5
Question : The areas of the two triangles are in the ratio 4 : 3 and their heights are in the ratio 6 : 5. Find the ratio of their bases.
Option 1: 5 : 6
Option 2: 10 : 9
Option 3: 6 : 5
Option 4: 9 : 10
Question : Two isosceles triangles have equal vertical angles and their areas are in the ratio 9 :16. Then the ratio of their corresponding heights is:
Option 1: 4.5 : 8
Option 2: 4 : 3
Option 3: 8 : 4.5
Option 4: 3 : 4
Question : The heights of two right circular cones are in the ratio 1 : 5 and the perimeter of their bases are in the ratio 5 : 3. Find the ratio of their volumes.
Option 1: 8 : 11
Option 2: 7 : 6
Option 3: 5 : 9
Question : The ratio of curved surface areas of two cones is 1 : 8 and the ratio of their slant heights is 1 : 4. What is the ratio of radii of the two cones?
Option 1: 1 : 1
Option 2: 1 : 2
Option 3: 1 : 4
Option 4: 1 : 8
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