Question : The ratio of the radii of two cylinders is $2:3$ and the ratio of their heights is $5:3$. The ratio of their volumes will be:
Option 1: $9:4$
Option 2: $20:27$
Option 3: $4:9$
Option 4: $27:20$
Correct Answer: $20:27$
Solution : Given: The ratio of the radii of two cylinders is $2:3$ and the ratio of their heights is $5:3$. Let the radii of the first cylinder = $2r$ units So, the radii of the second cylinder = $3r$ units Also, let their heights be $5h$ units and $3h$ units. The ratio of their volume, = $[\pi.(2r)^2.5h]:[\pi.(3r)^2.3h]$ = $[20\pi r^2h]:[27\pi r^2h]$ = $20:27$ Hence, the correct answer is $20:27$
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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 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
Option 4: 3 : 4
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
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 : The heights of two cones are in the ratio 7 : 5 and their diameters are in the ratio 10 : 21. What is the ratio of their volumes? (Where $\pi=\frac{22}{7}$)
Option 1: 26 : 47
Option 2: 14 : 19
Option 3: 20 : 63
Option 4: 17 : 21
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