Volumes And Surface Area

Volumes and surface area
BTEOTSSBAT solve problems involving volume and surface area

Key words
volume
cross section
prism
cube
cuboid
cylinder

Volume is the amount of space a solid object takes up.
The units are mm³, cm³, m³, km³ and so on
Convert m³ into cm³

A box has a volume of 0.5 m³.
It needs to fit into a bag of size 100 000 cm³. Will it fit?

0.5 m³ = 0.5 m x m x m

0.5 m³ = 0.5 m x m x m
x 100

0.5 m³ = 0.5 m x m x m
= 50 cm x m x m
x 100

0.5 m³ = 0.5 m x m x m
= 50 cm x m x m
x 100
x 100

0.5 m³ = 0.5 m x m x m
= 50 cm x m x m
x 100
x 100
= 5000 cm x cm x m

0.5 m³ = 0.5 m x m x m
= 50 cm x m x m
x 100
x 100
= 5000 cm x cm x m
x 100

0.5 m³ = 0.5 m x m x m
= 50 cm x m x m
x 100
x 100
= 5000 cm x cm x m
x 100
= 500 000 cm x cm x cm = cm³

0.5 m³ = 0.5 m x m x m
= 50 cm x m x m
x 100
x 100
= 5000 cm x cm x m
So, no it won’t fit!
x 100
= 500 000 cm x cm x cm = cm³

Prisms
Shapes that have a uniform cross section (ie all the same all the way through) are called prisms.
The volume of a prism is the cross-sectional area  length.

A square prism is called a cube

A rectangular prism is called a cuboid

A rectangular prism is called a cuboid
A circular prism is called a cylinder

Now try these
Find the volume of the following cuboids
4 cm
2 cm high 3 cm wide 2 cm
5 cm 3 cm
2. Computer disks are 9 cm by 0.3 cm by 9.3 cm. Calculate the volume of the disk.
3. A tin of beans has a diameter of 7 cm and is 4.5 cm high. Work out the volume of the tin.

Surface area
All 3D shapes have a surface area.
The surface area is the sum of the area of all the sides of a shape.
The surface area of a cuboid is the sum of all the 6 rectangular faces.
The rectangular faces can be grouped in pairs.

Example
Find the surface area of the cuboid which is 4 cm  5 cm  10 cm

Now try these
Find the surface areaof the following cuboids
4 cm
2 cm high 3 cm wide 2 cm
5 cm 3 cm
2. Computer disks are 9 cm by 0.3 cm by 9.3 cm. Calculate the surface areaof the disk.
3. A tin of beans has a diameter of 7 cm and is 4.5 cm high. Work out the surfaceof the tin.

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Volumes And Surface Area

by Steve Bishop on Nov 20, 2009

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