Questions from General Calculus

Q: A piece of wire 10 m long is cut into two pieces

A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is (a)...

Q: A fence 8 ft tall runs parallel to a tall building at

A fence 8 ft tall runs parallel to a tall building at a distance of 4 ft from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the...

Q: A cone-shaped drinking cup is made from a circular piece

A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and CB. Find the maximum capacity of such a cup.

Q: A cone-shaped paper drinking cup is to be made to

A cone-shaped paper drinking cup is to be made to hold 27 cm3 of water. Find the height and radius of the cup that will use the smallest amount of paper.

Q: A cone with height h is inscribed in a larger cone with

A cone with height h is inscribed in a larger cone with height H so that its vertex is at the center of the base of the larger cone. Show that the inner cone has maximum volume when h = 1/3H.

Q: (a). Show that of all the rectangles with a given

(a). Show that of all the rectangles with a given area, the one with smallest perimeter is a square. (b). Show that of all the rectangles with a given perimeter, the one with greatest area is a square...

Q: Find the limit. Use l’Hospital’s Rule where appropriate. If there

Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’...

Q: If a resistor of R ohms is connected across a battery of

If a resistor of R ohms is connected across a battery of E volts with internal resistance ohms, then the power (in watts) in the external resistor is If E and r, are fixed but R varies, what is the...

Q: For a fish swimming at a speed v relative to the water

For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v3. It is believed that migrating fish try to minimize the total energy required to swim...

Q: In a beehive, each cell is a regular hexagonal prism,

In a beehive, each cell is a regular hexagonal prism, open at one end with a trihedral angle at the other end as in the figure. It is believed that bees form their cells in such a way as to where s, t...