63-70 - Area of a Circular Sector These exercises involve the formula for the area of a circular sector. *.63. Find the area of the sector shown in each figure. (a) (b) 0.5 rad 80° 10 64. Find the radius of each circle if the area of the sector is 12. (a) (b) 0.7 rad 150° 65. Find the area of a sector with central angle 2/3 rad in a circle of radius 10 m. 66. A sector of a circle has a central angle of 145°. Find the area of the sector if the radius of the circle is 6 ft. 67. The area of a sector of a circle with a central angle of 140° is 70 m. Find the radius of the circle. 68. The area of a sector of a circle with a central angle of S7/12 rad is 20 m. Find the radius of the circle. 69. A sector of a cirele of radius 80 mi has an area of 1600 mi². Find the central angle (in radians) of the sector. 70. The area of a cirele is 600 m². Find the area of a sector of this cirele that subtends a central angle of 3 rad.
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
63–70 ■ Area of a Circular Sector These exercises involve the
formula for the area of a circular sector.
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