Find the area bounded by the curve x = y2 + 2y and the line x = 3.
Find the area bounded by the curve y = 9 - x2 and the x-axis.
The solid generated by rotating a plane area about an axis in its plane is called a solid of revolution. The volume of a solid of revolution may be found by the following procedures:
Plane Areas in Rectangular Coordinates
There are two methods for finding the area bounded by curves in rectangular coordinates. These are...
- by using a horizontal element (called strip) of area, and
- by using a vertical strip of area.
The strip is in the form of a rectangle with area equal to length × width, with width equal to the differential element. To find the total area enclosed by specified curves, it is necessary to sum up a series of rectangles defined by the strip.
Given the parabola 3x2 + 40y – 4800 = 0.
: What is the area bounded by the parabola and the X-axis?
A. 6 200 unit2
B. 8 300 unit2
C. 5 600 unit2
D. 6 400 unit2
: What is the moment of inertia, about the X-axis, of the area bounded by the parabola and the X-axis?
A. 15 045 000 unit4
B. 18 362 000 unit4
C. 11 100 000 unit4
D. 21 065 000 unit4
: What is the radius of gyration, about the X-axis, of the area bounded by the parabola and the X-axis?
A. 57.4 units
B. 63.5 units
C. 47.5 units
D. 75.6 units