A cubical box is to be built so that it holds 125 cu. How precisely should the edge be made so that the volume will be correct to within 3 cu cm?

A rectangular trough is 8 ft long, 2 ft across the top, and 4 ft deep. If water flows at the rate of 2 cu ft/min, how fast is the surface rising when the water is 1 ft deep?

Water is running out of a conical funnel at the rate of 1 cubic inch per sec. If the radius of the base of the funnel is 4 in and the altitude is 8 in, find the rate at which the water level is dropping when it is 2 in from the top.

Sand falls onto a conical pile at the rate of 10 cu.in/s. The radius of the base of the pile is always ½ of the altitude. How fast is the altitude of the pile increasing in in/s when it is 5 inches deep?

A stone is thrown into still water and causes concentric circular ripples. The radius of the ripples increases at the rate of 12 in/s. At what rate does the area of the ripples increases in sq. in/s when its radius is 3 inches?

A weight is attached to one end of a 33ft rope which passes over a pulley 18f above the ground. The other end is attached to a truck at a point 3ft above the ground. If the truck moves away at a rate of 2 ft/s, how fast in ft/s is the weight rising when the truck is 8ft from the spot directly under the pulley?

A conical vessel 12cm deep and with a radius of 6 cm at the top, is being filled with water. If the rate at which the water rises is 2cm/s, how fast is the volume increasing when the water is 4cm deep?

The volume of sphere is increasing at the rate of 6cc/hr. At what rate is the surface area increasing in sq.cm/hr when the radius is 50cm?

Two men A and B, start at the same point on the circumference of a circle 100m in radius. A runs at 10m/s while B runs at 8m/s in opposite direction. Find the rate at which the line distance between them is changing when the angle subtending them is 120°.

An open cylindrical through is constructed by bending a given sheet of tin and breadth 2a. Find the radius of the cylinder of which the trough forms a part when the capacity of the trough is a maximum.

Find the radius of a cylindrical measure and given a volume V so that the area of its sides and bottom shall be a minimum.

A piece of wire 36 cm long is cut in two, one part being bent in the shape of an equilateral triangle and the other in the form of a circle. Find the length of wire for the circle if the sum of the areas of these two figures is to be a minimum.

A cylindrical steam boiler is to be constructed having a capacity of 30 cu.m. The material for the side costs P25 per sq.m and for the ends P40 per sq.m. Find the radius for least cost.

The three sides of a trapezoid are each 10cm long, how long must the fourth side if the area is a maximum?

In how many equal parts can a wire 50cm long be cut so that the product of its parts is a maximum?

For a certain specified sum, a man takes the contract to build a rectangular water tank, lined with lead. It has a square base and open top and holds 108 cu.m. What should be the height of the tank that requires the least quantity of lead?

A person in a rowboat is 3km from a point P on a straight shore while his destination is 5km directly east of point P. If he is able to row 4kph and walk 5kph, how far from the destination must he land on the shore in order to reach his destination in the shortest possible time?

Find the minimum distance from the point (4, 2) to the parabola y2 = 8x.

What is the area of the largest rectangle that can be inscribed in a semi-circle of radius 10?

Two post, one 8m and the other 12m high are 15m apart. If the post are supported by wire running from the top of the first post to the stake on the ground and then back to the top of the second post, find the distance from the lower post to the stake to use minimum amount of wire.

A company owns a right triangular lot. The perpendicular sides are 90m and 60m. The company wants to construct a warehouse with a rectangular base of maximum area and with sides parallel to the perpendicular sides of the lot. Find the dimension of the base of the warehouse.

Find the radius of curvature of the ellipse 3x^2 + y^2 = 12 at the point (1,3)

When the energy/hour required in driving a boat varies as the cube of the velocity, find the most economical rate/hour when going against rest current of 4 kph.

What is the smallest positive value for x where y = sin 2x reaches i maximum.

Sand is being poured into a conical pile in such a way that the height is always 1/3 of the radius. At what rate is sand being added to the pile when it is 4 ft high if the height is increasing at 2 in/min.

A chord of a circle of a diameter 10 ft is decreasing in length 1 ft/min. Find the rate of change of the smaller arc subtended by the chord when the chord is 8ft long.

What percentage of the volume of a cone is the maximum volume right cylinder that can be inscribed in it?

A cardboard 20 in x 20 in is to be formed into a box by cutting four equal squares and folding the edges. Find the volume of the largest box.

Find the height of a right circular cylinder of maximum volume which can be inscribed in a sphere of radius 10 cm.

One end of a 32 m ladder resting on horizontal plane leans on a vertical wall. Assume the foot of the ladder to be pushed towards the wall at the rate of 2 m/min. How fast is the top of the ladder rising when its foot is 10m from the wall?