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The sum of the surface areas of a rectan...

The sum of the surface areas of a rectangualr parallelopiped with sides `x, 2 x` and `x/3` and a sphere is given to be constant. Prove that the sum of their volumes is minimum, if `x` is equal to three times the radius of the sphere. Also find the minimum value of the sum of their volumes.

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PRADEEP PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE
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  3. The total cost C (x) and the total revenue R (X) associated with the p...

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  4. The total revenue in Rupees received from the sale of x units of a pro...

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

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  6. Find the rate of change of the volume V of a sphere of radius r w.r.t ...

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  7. The radius of a balloon is increasing at the rate of 10 cm/sec. At wha...

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  8. The radius of a spherical soap bubble is increasing at the rate of 0.2...

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  9. A ballon, which always remains spherical has a variable diameter 3/2 (...

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  10. The volume of a spherical balloon is increasing at the rate of 20 cm^3...

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  11. An edge of a variable cube is increasing at the rate of 3 cm second. H...

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  12. A cone has a fixed radius r and a variable height h. Find the rate of ...

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  13. A right-circular cone has a fixed radius r and a variable height h. Fi...

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  14. A solid right circular cylinder has its radius equal to half of its he...

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  15. From a cylindrical drum containing oil and kept vertical, the oil leak...

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  16. Two men A and B start with velocities v at the same time from the junc...

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  17. A kite is moving horizontally at a height of 141.5 m. If the speed of ...

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  18. For what x, sinx increases half as fast as x?

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  19. A particle moves along the curve 6y = x^3+2. Find the points on the cu...

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  20. A man 160 cm tall, walks away from a source of light situated at the t...

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