A conical vessel is to be prepared out of a circular sheet of gold of unit radius. How much sectorial area is to be removed from the sheet so that the vessel has maximum volume?

A conical vessel is to be prepared out of a circular sheet of metal of unit radius in order that the vessel has maximum value, the sectorial area that must be removed from the sheet is A_(1) and the area of the given sheet is A_(2) , then A_(2)/A_(1) is equal to

From a circular aluminium sheet of radius 14 cm, a sector of angle 45^(@) is removed. Find the percentage of the area of the sector removed.

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. The lengths of the sides of the rectangular sheet are :

A concave mirror of radius of curvature R has a circular outline of radius r. A circular disc is to be placed normal to the axis at the focus so that it collects all the light that is reflected from the mirror from a beam parallel to the axis. For r gt gt R , the area of this disc has to be at least

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8: 15 is converted into anopen rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. Then the length of the sides of the rectangular sheet are 24 (b) 32 (c) 45 (d) 60

There is an infinite non conducting sheet of charge having uniform charge density sigma . The electric field at a point P at a distance x from the sheet is E_(0) . Point O is the foot of the perpendicular drawn from point P on the sheet. A circular portio of radius r lt lt x centered at O is removed from the sheet. Now the field at point P becomes E_(0)-DeltaE . Find DeltaE .

A square sheet of maximum area is cut out from a circular piece of carboard of radius 21 cm. Find the area of the remaining card board.

It takes 13.5 mL to paint the surface of the circular sheet of radius 17 cm . How much paint is required to paint a similar circular sheet with double the radius ?