Show that height of the cylinder of gre...

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle is one-third that of the cone and the greatest volume of cylinder is `4/(27)pih^3tan^2alphadot`

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Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle alpha is one - third that of the cone and the greatest volume of cylinder is (4pi)/(27)h^(3) tan^(2)alpha .

Prove that the radius of the right circular cylinder of greatest curved area which can be inscribed in a given cone is half of that of the cone.

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (2R)/(sqrt(3)) . Also find the maximum volume.

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is (4r)/(3) .

If the volume of a right circular cone of height 9 cm is 48 pi" "cm^(3) , find the diameter of its base.

Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is tan^(-1)sqrt(2) .

Find the volume of right circular cone with radius 6 cm and height 7 cm.

Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base.

A cylinder and a cone are of same base radius and of same height. Find the ratio of the volume of the cylinder to the volume of the cone.

Show that the right circular cone of least curved surface and given volume has an altitude equal to sqrt(2) time the radius of the base.

NCERT GUJARATI-APPLICATION OF DERIVATIVES-EXERCISE 6.6

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Find the intervals in which the function f given by f(x)=\ x^3+1/(...
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Find the maximum area of an isosceles triangle inscribed in the ellip...
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A tank with rectangular base and rectangular sides, open at the top...
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The sum of the perimeter of a circle and square is k, where k is so...
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A window is in the form of a rectangle surmounted by a semicircular...
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A point on the hypotenuse of a triangle is at distance a and b from t...
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Find the points at which the function f given by f(x)=(x-2)^4(x+1)^3 h...
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Find the absolute maximum and minimum values of the function f give...
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Show that the altitude of the right circular cone of maximum volume...
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Let f be a function defined on [a, b] such that f^(prime)(x)>0, for al...
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Show that the height of the cylinder of maximum volume that can be ...
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Show that height of the cylinder of greatest volume which can be insc...
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A cylindrical tank of radius 10 m is being filled with wheat at the r...
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The slope of the tangent to the curve x=t^(2)+3t-8,y=2t^(2) -2t -5 at...
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The line y = m x + 1is a tangent to the curve y^2=4xif the value of m...
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The normal at the point (1,1) on the curve 2y+x^2=3is(A) x + y = 0 (B)...
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The normal to the curve x^2=4ypassing (1,2) is(A) x + y = 3 (B) x y ...
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The points on the curve 9y^2=x^3, where the normal to the curve makes ...
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