Unit 10Unit 10

Cones & CylindersCones & CylindersUnit 10Unit 10

Cones & CylindersCones & Cylinders

Objective: To find the Objective: To find the Volume & Surface Area of Volume & Surface Area of

cones and cylinders.cones and cylinders.

Cylinders

Radius hrV 2Volum

eHeightradius

height

Volume of a Cylinder

Find the volume of a cylinder with height 10 cm and radius 5cm.

10 cm

5 cm

hrV 2

)10()5( 2V3cm 250V

3cm 785V

EXAMPLE #1

• Find the volume of the cylinder.

9 fthrV 2

)9()6( 2V3ft 324V

3ft 36.1017V

#2 you try!!!!

6 ft

Surface Area of a Cylinder

SA = 2r2 + 2rh

h

r

#3 Surface Area of a cylinder

Find the surface area of the cylinder with height of 9 m and radius of 3 m. Use 3.14. Round your answer to the nearest tenth.

rhrSA 22 2

)9)(3(2)3(2 2 SA

272

5418

mSA

SA

21.226 mSA

#4 YOU TRY!!!

Find the surface area of the cylinder with height of 5 m and radius of 8 m. Use 3.14. Round your answer to the nearest tenth.

rhrSA 22 2

)5)(8(2)8(2 2 SA

2208

80128

mSA

SA

21.653 mSA

Cones

Volume of a Cone

3

2hrV

Volume

Height

radius

r

h

THE VOLUME OF A CONE IS 1/3 THE VOLUME OF A CYLINDER.

3

2hrV

hrV 2

#5 Finding the Volume of a Cone

The radius of the base of a cone is 6 m. Its height is 13 m. Find the volume.

m 6

3

468V

3

)13(6 2V

3m 156V

m 133

2hrV

3m 84.489V

#6 YOU TRY!!!

The radius of the base of a cone is 4 m. Its height is 10 m. Find the volume.

m 43

160V

3

)10(4 2V

3m 3

160V

m 103

2hrV

3m 47.167V

Surface Area of a Cone

SA r l r 2

h

r

l

Slant height

radius radius

#7 Surface area of a cone

Find the surface area in terms of of a cone with a slant height of 19 cm and a radius of 5 cm. 2rrlSA

2)5()19)(5( SA

)25()95( SA2120 cmSA 28.376 cmSA

#8 YOU TRY!!!!

Find the surface area in terms of of a cone with a slant height of 15 cm and a radius of 4 cm. 2rrlSA

2)4()15)(4( SA

)16()60( SA276 cmSA

15 CM

4 CM26.238 cmSA

Sort according to shape (cylinders/cones)