Questions from General Calculus

Q: A right circular cylinder is inscribed in a sphere of radius r

A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible volume of such a cylinder.

Q: A right circular cylinder is inscribed in a cone with height h

A right circular cylinder is inscribed in a cone with height h and base radius r. Find the largest possible volume of such a cylinder.

Q: A right circular cylinder is inscribed in a sphere of radius r

A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible surface area of such a cylinder.

Q: A Norman window has the shape of a rectangle surmounted by a

A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle. See Exercise 1.1.62.) If the perimeter of the wind...

Q: The top and bottom margins of a poster are each 6 cm

The top and bottom margins of a poster are each 6 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 384 cm2, find the dimensions of the poster with the s...

Q: A poster is to have an area of 180 in2 with 1

A poster is to have an area of 180 in2 with 1-inch margins at the bottom and sides and a 2-inch margin at the top. What dimensions will give the largest printed area?

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: Answer Exercise 37 if one piece is bent into a square and

Answer Exercise 37 if one piece is bent into a square and the other into a circle. Exercise 37: A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent...

Q: If you are offered one slice from a round pizza (in

If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 32 inches, what diameter pizza will reward you with the largest slice?

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...