MEDIUM
12th West Bengal Board
IMPORTANT
Earn 100

A right circular cylinder is inscribed within a given sphere. Show that the height of the cylinder of maximum volume is 13 part of the diameter of the sphere. 

Important Questions on Maxima and Minima

MEDIUM
12th West Bengal Board
IMPORTANT
RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 19 - Maxima and Minima>EXERCISE>Q 29
Prove that the total surface area of right circular cylinder, open at one end, with a given volume is minimum when the height of the cylinder is same as the radius of its base.
HARD
12th West Bengal Board
IMPORTANT
RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 19 - Maxima and Minima>EXERCISE>Q 30
A rectangular box of volume 48 cu. ft. is to be constructed, so that its length is twice its width. The material to be used for the top and the four sides is three times costlier per sq. ft. than that used for the bottom. Show that the cost of construction of the box will be minimum when its height is equal to 83ft.
MEDIUM
12th West Bengal Board
IMPORTANT
RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 19 - Maxima and Minima>EXERCISE>Q 31
A wire of 28 metre length is cut into two pieces. A square is formed by bending one of these two pieces and the other is bent to form a circle. Determine the lengths of the pieces when the total area of the square and circle is minimum.
MEDIUM
12th West Bengal Board
IMPORTANT
RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 19 - Maxima and Minima>EXERCISE>Q 32
The length of each side of a square cardboard is 24cm. Four equal square portions are removed from the four corners of the board and the sides are then folded up to form an open box. Determine the height of the box when the volume contained in the box is maximum. 
HARD
12th West Bengal Board
IMPORTANT
RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 19 - Maxima and Minima>EXERCISE>Q 33
A window is in the shape of a rectangle with a semi-circular covering at the top. If the perimeter of the window be of a fixed length p. find its maximum area.
HARD
12th West Bengal Board
IMPORTANT
RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 19 - Maxima and Minima>EXERCISE>Q 34
Three sides of a trapezium are equal, each being a units. Find the maximum area of such a trapezium.
HARD
12th West Bengal Board
IMPORTANT
RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 19 - Maxima and Minima>EXERCISE>Q 35
The intensity of light varies inversely as the square of the distance from its source. There are two sources of light kept at a distance of 150 metres apart and one light is 8 times as bright as the other. Where should an object be placed between the lights so as to have the least illumination?
HARD
12th West Bengal Board
IMPORTANT
RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 19 - Maxima and Minima>EXERCISE>Q 36
A solid right circular cylinder of volume 2V and height h is sectioned by a plane passing through the centre of its base and perpendicular to the plane of the base. If r be the radius of the cylinder, prove that the surface area of each section is minimum when r=hπ+22π.