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A wire 10 meter long is cut into two par...

A wire 10 meter long is cut into two parts. One part is bent into the shape of a circle and the other into the shape of an equilateral triangle. How should the wire be cut so that the combined area of the two figures is as small as possible?

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PRADEEP PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE
  1. Prove that the area of right-angled triangle of given hypotenuse is ma...

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  2. Find the area of the largest isosceles triangle having perimeter 18 me...

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  3. A wire 10 meter long is cut into two parts. One part is bent into the ...

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  4. Show that a cylinder of given volume, open at the top, has minimum tot...

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  5. Find the altitude of the circular cylinder of maximum volume that can ...

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  6. Find the altitude of the circular cone of maximum volume that can be i...

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  7. Show that the semi-vertical angle of the right-circular cone of maximu...

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  8. The combined resistance of two resistors R1 and R@ (R1,R2>0) is given ...

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  9. Show that height of the cylinder of greatest volume which can be inscr...

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  10. Show that the surface area of a closed cuboid with surface base and gi...

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  11. A metal box with a square box and vertical sides is to contain 512 c^3...

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  12. An isosceles triangle of vertical angle 2theta is inscribed in a circl...

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  13. If the sum of the lengths of hypotenuse and a side of a right-angled t...

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  14. An open box with a square base is to be made out of a given iron sheet...

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  15. A point on the hypotenuse of a triangle is at distance a and b from th...

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  16. Find the dimensions of the rectangle of perimeter 36 cm which will swe...

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  17. If the sum of the surface areas of cube and a sphere is costnat, what ...

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  18. If the length of three sides of a trapezium other than base are equal ...

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  19. Find the shortest distance of the point (0, c) from the parabola y = x...

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  20. Let AP and BQ be two vertical poles at points A and B respectively. If...

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