1.4-1.6 1.4-1.6 Surface Area & Volume of Surface Area & Volume of

Prisms, Pyramids, Prisms, Pyramids, Cones and CylindersCones and Cylinders

Unit 3 – Math 10 CUnit 3 – Math 10 C

VolumeVolume

Volume is calculated by finding the Volume is calculated by finding the AREA of the BASE of a 3D object and AREA of the BASE of a 3D object and then multiplying by the height.then multiplying by the height.

The base of a 3D object is The base of a 3D object is perpendicular to its height.perpendicular to its height.

Volume is measured in unitsVolume is measured in units3 3

because the objects are three-because the objects are three-dimensional.dimensional.

Surface AreaSurface Area

Surface area is calculated by finding Surface area is calculated by finding the AREA of each SURFACE (go the AREA of each SURFACE (go figure!), and then adding them all figure!), and then adding them all together.together.

Surface Area is measured in unitsSurface Area is measured in units2 2

because the shapes are two-because the shapes are two-dimensional.dimensional.

What measurement would you use?What measurement would you use?

Painting your bedroomPainting your bedroom Putting up baseboardsPutting up baseboards Measuring the amount of air in your Measuring the amount of air in your

roomroom Laying carpetLaying carpet Wrapping a presentWrapping a present Mowing the lawnMowing the lawn Filling a juice canFilling a juice can Fencing off a fieldFencing off a field

Example 1: Surface AreaExample 1: Surface Area Find the surface area of the closed cylinder, Find the surface area of the closed cylinder,

correct to one decimal place.correct to one decimal place.

6.6 cm

6.6 cm

9.7 cm

22 2SA r rh

Example 2: Surface AreaExample 2: Surface Area The walls of Hana’s bedroom are to be The walls of Hana’s bedroom are to be

painted, except for the door, closet doors, painted, except for the door, closet doors, window floor and ceiling.window floor and ceiling.

1.1. Determine the area to be painted.Determine the area to be painted.

2.2. One can of paint covers 32 mOne can of paint covers 32 m22. How many . How many whole cans of paint are needed to apply two whole cans of paint are needed to apply two coats of paint to the walls?coats of paint to the walls?

Example 3: VolumeExample 3: Volume Hana would like to install an air conditioner in Hana would like to install an air conditioner in

her bedroom. her bedroom.

1.1. Determine the volume of air the air Determine the volume of air the air conditioner needs to circulate.conditioner needs to circulate.

BV A h V lwh

Now that her bedroom is done, Hana wants to test Now that her bedroom is done, Hana wants to test our her air conditioner in one of the many pyramids our her air conditioner in one of the many pyramids in Egypt. After a long plane ride (with her air in Egypt. After a long plane ride (with her air conditioner), she finally arrives. What is the volume conditioner), she finally arrives. What is the volume of cool air needed to completely cool this pyramid?of cool air needed to completely cool this pyramid?

3 m

6 m

4 m

1

3 BV A h

1

3V lwh

Example 5: VolumeExample 5: Volume The cylindrical pipe from a house to the main The cylindrical pipe from a house to the main

residential sewer line is 1 800 cm long with an residential sewer line is 1 800 cm long with an outside diameter of 16.0 cm and an inside diameter outside diameter of 16.0 cm and an inside diameter of 15.0 cm, as shown in the figure below.of 15.0 cm, as shown in the figure below.

1.1. Find the volume of the pipe as a solid cylinder of Find the volume of the pipe as a solid cylinder of material.material.

2.2. Determine the volume of the cylinder space inside Determine the volume of the cylinder space inside the pipe.the pipe.

3.3. Determine the volume of the material in the pipe to Determine the volume of the material in the pipe to the nearest cubic centimetre.the nearest cubic centimetre.

1800 cm

15 cm

16 cm

1.9 Surface Area and 1.9 Surface Area and Volume of a SphereVolume of a Sphere

Unit 1 – Math 10AUnit 1 – Math 10A

Surface AreaSurface Area

r24SA r

Determine the surface area of a Determine the surface area of a volleyball that has a diameter of 22 volleyball that has a diameter of 22 cm.cm.

VolumeVolume

Determine the volume of a volleyball Determine the volume of a volleyball that has a diameter of 22 cm.that has a diameter of 22 cm.

34

3V r r