Questions from General Calculus

Q: The height of a monument is 20 m. A horizontal cross

The height of a monument is 20 m. A horizontal cross section at a distance x meters from the top is an equilateral triangle with / meters. Find the volume of the monument.

Q: (a) The base of a solid is a square with

(a) The base of a solid is a square with vertices located at (1, 0), (0, 1), (21, 0), and (0, 21). Each cross-section perpendicular to the x-axis is a semicircle. Find the volume of the solid. (b) Sho...

Q: A 1600-lb elevator is suspended by a 200-ft

A 1600-lb elevator is suspended by a 200-ft cable that weighs 10 lb/ft. How much work is required to raise the elevator from the basement to the third floor, a distance of 30 ft?

Q: A tank full of water has the shape of a paraboloid of

A tank full of water has the shape of a paraboloid of revolution as shown in the figure; that is, its shape is obtained by rotating a parabola about a vertical axis. (a) If its height is 4 ft and the...

Q: A steel tank has the shape of a circular cylinder oriented vertically

A steel tank has the shape of a circular cylinder oriented vertically with diameter 4 m and height 5 m. The tank is currently filled to a level of 3 m with cooking oil that has a density of 920 kg/m3....

Q: (a) Find the average value of the function f(

(a) Find the average value of the function f(x) – 1/sx on the interval [1, 4]. (b) Find the value c guaranteed by the Mean Value Theorem for Integrals such that fave = f(c). (c) Sketch the graph of f...

Q: Let R1 be the region bounded by y = x2 , y

Let R1 be the region bounded by y = x2 , y = 0, and (a) Is there a value of b such that /1 and /2 have the same area? (b) Is there a value of b such that /1 sweeps out the same volume when rotated ab...

Q: Find the area of the region bounded by the given curves.

Find the area of the region bounded by the given curves.

Q: Sketch the region enclosed by the given curves and find its area

Sketch the region enclosed by the given curves and find its area.

Q: A cylindrical glass of radius r and height L is filled with

A cylindrical glass of radius r and height L is filled with water and then tilted until the water remaining in the glass exactly covers its base. (a) Determine a way to “sliceâ...