CK-12 Geometry Concepts

11.4. Cylinders http://www.ck12.org

3. This solid is a parallelogram-based prism with a cylinder cut out of the middle. To find the volume, we need to
   find the volume of the prism and then subtract the volume of the cylinder.

Vprism= ( 25 · 25 ) 30 = 18750 cm^3

Vcylinder=π( 4 )^2 ( 30 ) = 480 πcm^3

The total volume is 18750− 480 π≈ 17242. 04 cm^3.

Practice

1. The lateral surface area of a cylinder is what shape? What is the area of this shape?


2. A right cylinder has a 7 cm radius and a height of 18 cm. Find the surface area and volume.

Find the surface area and volume of the following solids. Leave answers in terms ofπ.

3.

4.

Find the value ofx, given the surface area.

5.SA= 1536 πunits^2

6. The area of the base of a cylinder is 25πin^2 and the height is 6 in. Find thelateralsurface area.


7. The circumference of the base of a cylinder is 80πcmand the height is 36 cm. Find the total surface area.


8. The lateral surface area of a cylinder is 30πm^2. What is one possibility for height of the cylinder?


9. Charlie started a business canning artichokes. His cans are 5 in tall and have diameter 4 in. If the label
   must cover the entire lateral surface of the can and the ends must overlap by at least one inch, what are the
   dimensions and area of the label?


10. Find an expression for the surface area of a cylinder in which the ratio of the height to the diameter is 2:1. If
    xis the diameter, use your expression to findxif the surface area is 160π.


11. Two cylinders have the same surface area. Do they have the same volume? How do you know?


12. A can of soda is 4 inches tall and has a diameter of 2 inches. How much soda does the can hold? Round your
    answer to the nearest hundredth.


13. A cylinder has a volume of 486πf t.^3. If the height is 6 ft., what is the diameter?


14. The area of the base of a cylinder is 49πin^2 and the height is 6 in. Find the volume.


15. The circumference of the base of a cylinder is 80πcmand the height is 15 cm. Find the volume.


16. The lateral surface area of a cylinder is 30πm^2 and the circumference is 10πm. What is the volume of the
    cylinder?