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प्रश्न
The `3/4` th part of a conical vessel of internal radius 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height of water in cylindrical vessel.
उत्तर
Radius of conical vessel r = 5 cm
Height of conical vessel h = 24 cm
The volume of water = `3/4` ×volume of conical vessel
`= 3/4 xx 1/3 pir^2h`
`3/4 xx 1/3 pi xx 25 xx 24`
= 150
Let h' be the height of cylindrical vessel, which filled by the water of conical vessel,
Radius of cylindrical vessel = 10 cm
Clearly,
Volume of cylindrical vessel = volume of water
`pi(10)^2h = 150`
=> h = 1.5 cm
Thus, the height of cylindrical vessel is 1.5 cm.
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The ratio between the volume of two spheres is 8 : 27. What is the ratio between their surface areas?
Assertion (A)
If the volumes of two spheres are in the ratio 27 : 8, then their surface areas are in the ratio 3 : 2.
Reason (R)
Volume of a sphere `=4/3pi"R"^3`
Surface area of a sphere = 4πR2
Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).- Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
- Assertion (A) is true and Reason (R) is false.
- Assertion (A) is false and Reason (R) is true.
