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Sand is pouring from a pipe at the rate of`12\ c m^3//s` . The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?

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The correct Answer is:
`(1)/(48pi)` cm /s
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NCERT GUJARATI-APPLICATION OF DERIVATIVES-EXERCISE 6.1
  1. Find the rate of change of the area of a circle with respect to its ra...

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  2. The volume of a cube is increasing at the rate of 8 c m^3//s. How fast...

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  3. The radius of a circle is increasing uniformly at the rate of 3 cm/...

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  4. An edge of a variable cube is increasing at the rate of 3 cm//s. How f...

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  5. A stone is dropped into a quiet lake and waves move in circles at the ...

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  6. 6. The radius of a circle is increasing at the rate of 0.7 cm/s. What ...

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  7. The length x of a rectangle is decreasing at the rate of 5 cm/minut...

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  8. A balloon, which always remains spherical on inflation, is being in...

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  9. A balloon, which always remains spherical, has a variable radius. F...

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  10. A ladder 5 m long is leaning against a wall. The bottom of the ladd...

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  11. A particle moves along the curve 6y = x^(3)+2. Find the points on th...

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  12. The radius of an air bubble is increasing at the rate of 1/2c m//s. A...

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  13. A balloon, which always remains spherical, has a variable diameter 3/...

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  14. Sand is pouring from a pipe at the rate of12\ c m^3//s . The falling s...

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  15. The total cost C (x) in Rupees associated with the production of x un...

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  16. The total revenue in Rupees received from the sale of x units of a pr...

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  17. The rate of change of the area of a circle with respect to its radius ...

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  18. The total revenue in Rupees received from the sale of x units of a pr...

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