tailieunhanh - Lecture General mathematics: Lecture 26 - Ms. Fehmida Haroon

Lecture you will review how the second derivative of a function is related to the shape of its graph and how that information can be used to classify relative extreme values. This chapter presents the following content: Concavity and points of inflection, the second derivative test, graphing polynomials. | General Mathematics ADE 101 Unit 3 LECTURE No. 26 SURFACE AREA AND VOLUME OF CYLINDER 1 Today’s Objectives Knowledge Test The circumference of a circle is the perimeter of the circle. Imagine that the circle is straightening itself out. The length of this line segment is the circumference of the circle. 314 cm The circumference is the same length as 3 diameters plus .14 of another diameter. So, circumference = diameter x Does this look familiar? Remember, area is always measured in square units. Remember that the area of a rectangle is length x width because you’re calculating the total number of squares inside of the rectangle. 2 4 That’s fine and dandy, but a circle is not a polygon. It does not have straight sides; it has curves. How are we going to get around these curves? Imagine chopping up the circle as if it were a pizza. Now, let’s rearrange our “pizza” into another shape. Area = Base x Height Base Height To find the area of the circle (which is now a parallelogram), we just need to multiply the Base by the Height. Base Height Base Radius The height of this “parallelogram” is really the radius of the circle. 1/2 of Circumference Radius The Base is really 1/2 of the circumference. 1/2 of Diameter x Radius The circumference is really Diameter x Radius x Radius 1/2 of a Diameter is really a Radius. Base Height So if we multiply the Base x Height Radius x Radius We are really multiplying Radius x Radius x 1) Now let’s try this formula. Find the area of this circle. 5 cm 5 x 5 x = square cm 5 cm 2) Find the area of this circle. 6 cm 6 x 6 x = square cm 6 cm 3) Find the area of this circle. 9 cm 9 x 9 x = square cm 9 cm 5) Find the area of this circle. 14 cm 7 x 7 x = cm2 14 cm Make sure that you use the radius of the circle. Cylinder Volume of a Cylinder Label the BASE and HEIGHT of the cylinder below: Base of the Cylinder! Height of the Cylinder! For the Volume of a Cylinder we can write: V = B(h) OR | General Mathematics ADE 101 Unit 3 LECTURE No. 26 SURFACE AREA AND VOLUME OF CYLINDER 1 Today’s Objectives Knowledge Test The circumference of a circle is the perimeter of the circle. Imagine that the circle is straightening itself out. The length of this line segment is the circumference of the circle. 314 cm The circumference is the same length as 3 diameters plus .14 of another diameter. So, circumference = diameter x Does this look familiar? Remember, area is always measured in square units. Remember that the area of a rectangle is length x width because you’re calculating the total number of squares inside of the rectangle. 2 4 That’s fine and dandy, but a circle is not a polygon. It does not have straight sides; it has curves. How are we going to get around these curves? Imagine chopping up the circle as if it were a pizza. Now, let’s rearrange our “pizza” into another shape. Area = Base x Height Base Height To find the area of the circle (which is now a parallelogram), we

• Toán học
• General mathematics
• Lecture General mathematics
• Geometric measurement
• Algebraic thinking
• Mathematical knowledge
• Constant functions
• Number pattern
• Cartesian coordinate system
• Liner equations
• Graph of liner equations
• Linear equation
• Natural numbers