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