An inverted cone has a depth of 40 cm and a base of radius 5cm .water is poured into it at a rate of 3/2 cubic centimetres per minute.find the rate at which the level of water in the cone is rising when the depth is 4 cm ..

. An open tank with a square base and vertical sides is to be constructed from a metalsheet so as to hold a given quantity of water. Show that the total surface area is least when depth of the tank is half its width.(2010c)

Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.

at what points of the ellipse 16x^2 + 9y^2 = 400 does the ordinate decrease at the same rate at which the abcissa increases ??

prove : semi verticle angle of right circular cone of given volume and least curved surface area is cot^-1 (root2) .

find the equation of tangent and normal to the curve x=1-cos theta, y= theta-sin theta at theta=pi/4.

find the point on the parabola y=x^2 + 7x+2 which is closest to the straight line y=3x-3.

Show that the area of the triangle formed by the tangent and the normal at tha point(a,a) on tha curve y^{2}(2a-x)=x^{3} and the line x=2a,is 5a^{2/}4.

Prove that the curves x = y^{2} and xy = k cut at right angles if 8k^{2} = 1. [Hint: Two curves intersect at right angle if the tangents to the curves at the point of intersection are perpendicular to each other.]

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 α is one-third that of the cone and the greatest volume of cylinder istan^{2}α.

show that the condition that the curves ax^{2}+by^{2}=1 and a'x^{2}+b'y^{2}=1 should intersect orthogonally (at90^{0}) such that 1/a-1/b=1/a'-1/b'

A wire of length 36cm is cut into two pieces,one of the pieces is turned in d form of a square and d other in d form of equilatral tringle.find the length of each piece so that d sum of areas of d two be minimum.? reply fast.

A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2 cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall?

show that the right circular cone of least curved surface area and given volume has an altitude equal to root 2 times the radius of the base.

An inverted cone has a depth of 40 cm and a base of radius 5cm .water is poured into it at a rate of 3/2 cubic centimetres per minute.find the rate at which the level of water in the cone is rising when the depth is 4 cm ..

. An open tank with a square base and vertical sides is to be constructed from a metalsheet so as to hold a given quantity of water. Show that the total surface area is least when depth of the tank is half its width.(2010c)

Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.

at what points of the ellipse 16x^2 + 9y^2 = 400 does the ordinate decrease at the same rate at which the abcissa increases ??

prove : semi verticle angle of right circular cone of given volume and least curved surface area is cot^-1 (root2) .

find the equation of tangent and normal to the curve x=1-cos theta, y= theta-sin theta at theta=pi/4.

find the point on the parabola y=x^2 + 7x+2 which is closest to the straight line y=3x-3.

Show that the area of the triangle formed by the tangent and the normal at tha point(a,a) on tha curve y

^{2}(2a-x)=x^{3}and the line x=2a,is 5a^{2/}4.Prove that the curves

x=y^{2}andxy = kcut at right angles if 8k^{2}= 1. [Hint: Two curves intersect at right angle if the tangents to the curves at the point of intersection are perpendicular to each other.]ind the coordinate of a point on the parabola y=x^{2 }+7x+2 which is closest to the straight line y=3x-3?Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height

hand semi vertical angleαis one-third that of the cone and the greatest volume of cylinder istan^{2}α.show that the condition that the curves ax

^{2}+by^{2}=1 and a'x^{2}+b'y^{2}=1 should intersect orthogonally (at90^{0}) such that 1/a-1/b=1/a'-1/b'A wire of length 36cm is cut into two pieces,one of the pieces is turned in d form of a square and d other in d form of equilatral tringle.find the length of each piece so that d sum of areas of d two be minimum.? reply fast.

A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2 cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall?

show that the right circular cone of least curved surface area and given volume has an altitude equal to root 2 times the radius of the base.