7.4: SURFACE AREA AND VOLUME OF CYLINDERS Expectation: G1.8.1: Solve multistep problems involving...
19
7.4: Surface Area and Volume of Cylinders Expectation: G1.8.1: Solve multistep problems involving surface area and volume of pyramids, prisms, cones, cylinders, hemispheres, and spheres. 05/08/22 7.4: Surface Area and Volume of Cylinders
-
Upload
neil-bryan -
Category
Documents
-
view
226 -
download
0
Transcript of 7.4: SURFACE AREA AND VOLUME OF CYLINDERS Expectation: G1.8.1: Solve multistep problems involving...
7.4: Surface Area and Volume of Cylinders
Expectation:G1.8.1: Solve multistep problems involving surface area and volume of pyramids, prisms, cones, cylinders, hemispheres, and spheres.
05/05/23 7.4: Surface Area and Volume of Cylinders
A regular hexagonal pyramid has base perimeter of 72 inches and slant height of 14 inches. Determine the exact volume of the pyramid.
What will we learn today?
05/05/23 7.4: Surface Area and Volume of Cylinders
Cylinder
Defn: A cylinder is the union of a circular region, its translated image in space and all points in between.
05/05/23 7.4: Surface Area and Volume of Cylinders
Anatomy of a Cylinder
05/05/23 7.4: Surface Area and Volume of Cylinders
_________
Anatomy of a Cylinder
05/05/23 7.4: Surface Area and Volume of Cylinders
Lateral surface
Anatomy of a Cylinder
05/05/23 7.4: Surface Area and Volume of Cylinders
_________
The height of a cylinder is the length of one of its altitudes.
Anatomy of a Cylinder
05/05/23 7.4: Surface Area and Volume of Cylinders
The ______of a cylinder is the segment with its endpoints at the centers of the bases.
Right Cylinders
A cylinder is right if its axis is ______________ to its bases.
05/05/23 7.4: Surface Area and Volume of Cylinders
Oblique Cylinders
A cylinder is oblique if its axis is oblique to its ______.
05/05/23 7.4: Surface Area and Volume of Cylinders
Lateral and Surface Areas of a Right Cylinder
a. Sketch a net for a right cylinder with radius r and height h.b. What is the lateral area of the cylinder?c. What is the surface area of the cylinder?
05/05/23 7.4: Surface Area and Volume of Cylinders
Lateral and Surface Areas of a Right Cylinder
Let L be the lateral area and S be the surface area of a right cylinder with radius r and height h. Then L = _______ and S = ______________
05/05/23 7.4: Surface Area and Volume of Cylinders
Volume of a Cylinder
Let V be the volume of a cylinder with radius r and height h. Then V=_________.
05/05/23 7.4: Surface Area and Volume of Cylinders
A cylindrical water tank has a diameter of 30 feet and a height of 100 feet. If 1 cubic foot of water is 7.48 gallons, how many gallons of water will the tank hold?
05/05/23 7.4: Surface Area and Volume of Cylinders
An oblique cylinder has a height of 10 inches and its base has radius of 5 inches. A Right cylinder has radius of 5 inches and its height is 10 inches. A right rectangular prism has a base with dimensions 5 inches by 5π inches and a height of 10 inches. Compare the volumes of the three figures and give a justification.
05/05/23 7.4: Surface Area and Volume of Cylinders
The volume of a right cylinder is 125π cubic cm. If the height of the cylinder is 5 cm, what is the surface area of the right cylinder?
05/05/23 7.4: Surface Area and Volume of Cylinders
What is the volume of a cylinder with a height of 16 and a base area of 25π?A.5πB.25πC.50πD.200πE.400π
05/05/23 7.5: Surface Area and Volume of Cones
Assignment
pages 456-458, # 13-29(odd), 30-32 (all), 35-38
05/05/23 7.4: Surface Area and Volume of Cylinders
